Steven J. Miller                                                      
Professor of Mathematics, Williams College               
18 Hoxsey St, Williamstown, MA 01267
(sjm1 AT williams.edu)

NOTE: At some point my pages will be migrating to https://sites.williams.edu/sjm1/
 
 [Click here for my schedule]    [Click here for general advice]

 curriculum vita (click here for annotated bibliography)
research statement       and     teaching statement
 Takeaways (all classes)   
   Welcome letter to Williams Students
Possible thesis / colloquium projects
Opportunities in Mathematics (REUs, gradschool)
photos of Cam and Kayla
RESEARCH INTERESTS:  Analytic Number Theory, Random Matrix Theory, Probability (zeros and n-level statistics for families of L-functions, especially families of elliptic curves with rank over Q(T), classical random matrix theory, random graphs, computational number theory, Benford's Law, cryptography, linear programming, sabermetrics, ...).

      Thesis         Papers        Talks     Books:  Invitation Modern Number Theory           Mathematics of Encryption        Benford's Law       Handouts      My Riddles Page  

ACCEPTED  PAPERS   

  1. 1- and 2-level densities for rational families of elliptic curves: evidence for the underlying group symmetries. Compositio Mathematica (140 (2004), no. 4, 952--992).    pdf
  2. Distribution of eigenvalues for the ensemble of real symmetric Toeplitz matrices (with Chris Hammond). Journal of Theoretical Probability (18 (2005), no. 3, 537-566).   pdf
  3. Benford's law, values of L-functions and the 3x+1 problem (with Alex Kontorovich), Acta Arithmetica. (120 (2005), no. 3, 269--297).  pdf.
  4. Variation in the number of points on elliptic curves and applications to excess rank, C. R. Math. Rep. Acad. Sci. Canada (27 (2005), no. 4, 111--120, Expanded Version). pdf
  5. Incomplete exponential sums in several variables (with Eduardo Duenez, Howard Straubing, and Amitahba Roy), Journal of Number Theory (116 (2006), no. 1, 168--199). pdf
  6. Closed-form Bayesian inferences for the logit model via polynomial expansions (with Eric Bradlow and Kevin Dayaratna), Quantitative Marketing and Economics (4 (2006), no. 2, 173--206).   pdf

  7. Investigations of zeros near the central point of elliptic curve L-functions, Experimental Mathematics (15 (2006), no. 3, 257--279).  pdf  (data available online).

  8. The low-lying zeros of a GL(4) and a GL(6) family of L-functions (with Eduardo Duenez), Compositio Mathematica (142 (2006), no. 6, 1403--1425) pdf.
  9. Low-lying zeros of L-functions with orthogonal symmetry (with Chris Hughes), Duke Mathematical Journal (136 (2007), no. 1, 115--172)   pdf
  10. Constructing one-parameter families of elliptic curves over Q(T) with moderate rank (with Scott Arms, Alvaro Lozano-Robledo), Journal of Number Theory. (123 (2007), no 2, 388--402   pdf
  11. A derivation of James' Pythagorean projection, By The Numbers -- The Newsletter of the SABR Statistical Analysis Committee (16 (February 2006), no. 1, 17--22).   pdf (expanded version: pdf).  Chance (20 (Winter 2007), no. 1, 40-48).
  12. Distribution of eigenvalues of real symmetric palindromic Toeplitz matrices and circulant matrices (with Adam Massey and John Sinsheimer), Journal of Theoretical Probability. (20 (2007), no. 3, 637--662.)  pdf
  13. Benford's Law applied to hydrology data - results and relevance to other geophysical data (with Mark Nigrini), Mathematical Geology (39 (2007), no. 5, 469--490).  pdf
  14. When the Cramer-Rao Inequality provides no information, Communications in Information and Systems.  (7 (2007), no. 3, 265--272).   pdf
  15. The Modulo 1 Central Limit Theorem and Benford's Law for Products (with Mark Nigrini), International Journal of Algebra. (2 (2008), no. 3, 119--130). pdf
  16. A Symplectic Test of the L-Functions Ratios Conjecture, IMRN (2008). (Vol. 2008, article ID rnm146, 36 pages, doi:10.1093/imrn/rnm146).   pdf
  17. An identity for sums of polylogarithm functions, Integers (electronic journal of combinatorial number theory). (8 (2008), A15)   pdf
  18. A probabilistic proof of Wallis' formula for π, American Mathematical Monthly. (115 (2008), no. 8, 740--745)   pdf
  19. The distribution of the second largest eigenvalue in families of random regular graphs (with Tim Novikoff and Anthony Sabelli), Experimental Mathematics. (17 (2008), no. 2, 231--244.)  pdf
  20. Order statistics and Benford's law (with Mark Nigrini), International Journal of Mathematics and Mathematical Sciences (Volume 2008 (2008), Article ID 382948, 19 pages, doi:10.1155/2008/382948)  pdf
  21. Lower order terms in the 1-level density for families of holomorphic cuspidal newforms, Acta Arithmetica. (137 (2009), 51-98)  pdf
  22. Chains of distributions, hierarchical Bayesian models and Benford's Law (with D. Jang, J. U. Kang, A. Kruckman and J. Kudo), Journal of Algebra, Number Theory: Advances and Applications. (volume 1, number 1 (March 2009), 37--60)   pdf
  23. An orthogonal test of the L-functions Ratios Conjecture, London Mathematical Society. (2009, doi:10.1112/plms/pdp009)   pdf
  24. Silver Scheduler: Demand-Driven Scheduling of Movies in a Multiplex (with Jehoshua Eliashberg, Quintus Hegie, Jason Ho, Dennis Huisman, Sanjeev Swami, Charles B. Weinberg and Berend Wierenga), lead article International Journal of Market Research and won award for best paper of 2009 (doi:10.1016/j.ijresmar.2008.09.004)  pdf
  25. The effect of convolving families of L-functions on the underlying group symmetries (with Eduardo Duenez), Proceedings of the London Mathematical Society. (2009; doi: 10.1112/plms/pdp018)   pdf
  26. When almost all sets are difference dominated (with Peter Hegarty), Random Structures and Algorithms. (35, 2009, no. 1, 118-136)   pdf 
  27. Nuclei, primes and the random matrix connection (with Frank W. K. Firk), invited paper to Symmetry (1, (2009), 64--105; doi:10.3390/sym1010064)   pdf
  28. Data diagnostics using second order tests of Benford's Law (with Mark Nigrini), Auditing: A Journal of Practice and Theory.  (28 (2009), no. 2, 305--324. doi: 10.2308/aud.2009.28.2.305)  MSWord file
  29. Explicit constructions of infinite families of MSTD sets (with Brooke Orosz and Dan Scheinerman), Journal of Number Theory (130 (2010) 1221--1233) pdf
  30. A unitary test of the L-functions Ratios Conjecture (with John Goes, Steven Jackson, David Montague, Kesinee Ninsuwan, Ryan Peckner and Thuy Pham), Journal of Number Theory. (130 (2010) 2238--2258)  pdf
  31. Towards an `average' version of the Birch and Swinnerton-Dyer Conjecture (with John Goes), Journal of Number Theory (130 (2010), no. 10, 2341--2358)    pdf
  32. An Orthogonal Test of the L-functions Ratios Conjecture, II (with David Montague),  Acta Arithmetica  (146 (2011), 53--90.)  pdf
  33. Rational irrational proofs (with David Montague), Mathematics Magazine (85 (2012), no. 2, 110--114).  pdf (expanded version: pdf;    letter from Nerode and Tennenbaum on history of proof: pdf)
  34. Explicit constructions of infinite families of MSTD sets (with Dan Scheinerman), Additive Number Theory: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson, David Chudnovsky and Gregory Chudnovsky (Editors), Springer-Verlag, 2010. pdf
  35. Demand-driven scheduling of movies in a multiplex (with Jehoshua Eliashberg and Charles B. Weinberg), newsletter of the European Marketing Academy, October 2010 (requested summary of Silver-Scheduler paper in honor of it receiving the International Journal of Market Research Best Paper Award for 2009).
  36. Effective equidistribution and the Sato-Tate law for families of elliptic curves (with M. Ram Murty), Journal of Number Theory (131 (2011), no. 1, 25-44)   pdf
  37. The lowest eigenvalue in Jacobi ensembles and Painleve VI (with Eduardo Duenez, Duc Khiem Huynh, Jon Keating and Nina Snaith), Journal of Physics A: Mathematical and Theoretical (43 (2010), 405204, 27pages)   pdf
  38. Isoperimetric Sequences (with Frank Morgan, Edward Newkirk and Lori Pedersen), Mathematics Magazine (84 (Feb. 2011), 37--42).  pdf
  39. Distribution of eigenvalues for highly palindromic real symmetric Toeplitz matrices (with Steven Jackson and Thuy Pham), Journal of Theoretical Probability. (25 (2012), 464--495)   pdf
  40. A combinatorial identity for studying Sato-Tate type problems (with M. Ram Murty and F. Strauch), Rendiconti del Seminario Matematico (68 (2010), no. 4, 337--348).  pdf
  41. Moments of the rank of elliptic curves (with Siman Wong), Canadian Journal of Mathematics (64 (2012), no. 1, 151--182)    pdf
  42. The `Real' Schwarz lemma (with David Thompson):  American Mathematical Monthly. (118 (October 2011), no. 8, page 725)   pdf
  43. An elliptic curve family test of the Ratios Conjecture (with Duc Khiem Huynh and Ralph Morrison), Journal of Number Theory (131 (2011), 1117--1147)  pdf
  44. On the number of summands in Zeckendorf decompositions (with Gene S. Kopp, Murat Koloğlu and Yinghui Wang), Fibonacci Quarterly. (49 (2011), no 2, 116--130)   pdf
  45. Generalized More Sums Than Differences Sets (with Geoffrey Iyer, Oleg Lazarev and Liyang Zhang), Journal of Number Theory. (132 (2012), no. 5, 1054--1073) pdf 
  46. Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets (with Luc Robinson and Sean Pegado). INTEGERS (12, #A30 2012). pdf
  47. Models for zeros near the central point of families of elliptic curves (with Eduardo Duenez, Duc Khiem Huynh, Jon Keating and Nina Snaith), Journal of Physics A: Mathematical and Theoretical (45 (2012),  115207 (32pp)).  pdf
  48. From Fibonacci Numbers to Central Limit Type Theorems (with Yinghui Wang), Journal of Combinatorial Theory, Series A. (7 (2012), 1398-1413)   pdf    (expanded arxiv version)
  49. First Order Approximations of the Pythagorean Won-Loss Formula for Predicting MLB Teams Winning Percentages (with Kevin Dayaratna), By The Numbers -- The Newsletter of the SABR Statistical Analysis Committee,   pdf (expanded version with appendix proving main result with just one variable calculus: pdf); entire issue of By The Numbers here (22 (2012), no 1, 15--19).
  50. Low-lying zeros of number field L-functions (with Ryan Peckner), Journal of Number Theory.  (132 (2012), 2866--2891) pdf
  51. Quadratic fields with cyclic 2-class groups (with Carlos Dominguez and Siman Wong): Journal of Number Theory (133 (2013), no. 3, 926--939).   pdf
  52. Leading, learning and herding (with Daniel Stone), Mathematical Social Sciences (65 (2013), 222--231)  pdf
  53. The Pythagorean Won-Loss Formula and Hockey: A Statistical Justification for Using the Classic Baseball Formula as an Evaluative Tool in Hockey (with Kevin Dayaratna), The Hockey Research Journal: A Publication of the Society for International Hockey Research. ((2012/2013), pages 193--209)   pdf
  54. The Average Gap Distribution for Generalized Zeckendorf Decompositions (with Olivia Beckwith, Amanda Bower, Louis Gaudet, Rachel Insoft, Shiyu Li and Philip Tosteson), the Fibonacci Quarterly (51 (2013), 13--27). pdf
  55. Closed Form Continued Fraction Expansions of Special Quadratic Irrationals (with Dan Fishman), ISRN Combinatorics. (vol. 2013, Article ID 414623, 5 pages)  pdf (journal version)
  56. Distribution of Missing Sums in Sumsets (with Oleg Lazarev and Kevin O'Bryant), Experimental Mathematics (22 (2013), no. 2, 132--156).  pdf
  57. The n-level densities of low-lying zeros of quadratic Dirichlet L-function (with Jake Levinson), Acta Arithmetica. (161 (2013), 145--182)   pdf   (Mathematica files available here)
  58. Viruslike dynamics on starlike graphsviruslike dynamics on starlike graphs (with Thealexa Becker, Alec Greaves-Tunnell, Leo Kontorovich, Amitabha Roy, Karen Shen), the Journal of Nonlinear Systems and Applications (4 2013), no. 153--63). pdf
  59. The Limiting Spectral Measure for Ensembles of Symmetric Block Circulant Matrices (with Gene S. Kopp Murat Koloğlu, Frederick Strauch, Wentao Xiong). Journal of Theoretical Probability  (26 (2013), no. 4, 1020--1060) pdf
  60. Coordinate sum and difference sets of d-dimensional modular hyperbolas (with Amanda Bower, Ron Evans and Victor Luo),  INTEGERS (#A31, 2013, 16 pages)  pdf  (expanded arxiv version: pdf)
  61. The Pi Mu Epsilon 100th Anniversary Problems: Part I (with James M. Andrews, Avery T. Carr and many of my students), The Pi Mu Epsilon Journal (13 (2013), no. 9, 513--534). pdf
  62. The low-lying zeros of level 1 Maass forms (with Levent Alpoge), IMRN. (2014, 24 pages, doi:10.1093/imrn/rnu012) pdf
  63. Special Sets of Primes in Function Fields (with Julio Andrade, Kyle Pratt and Minh-Tam Trinh), INTEGERS. (14 (2014), #A18) pdf 
  64. Generalizing Zeckendorf's Theorem to \(f\)-decompositions (joint with Philippe Demontigny, Thao Do, Archit Kulkarni, David Moon and Umang Varma), Journal of Number Theory. (141 (2014), 136--158)  pdf
  65. Pythagoras at the Bat (with Taylor Corcoran, Jen Gossels, Victor Luo and Jaclyn Porfilio), book chapter in Social Networks and the Economics of Sports (edited by Panos M. Pardalos and Victor Zamaraev, Springer-Verlag, 2014, pages 89--114).  pdf
  66. A Generalization of Fibonacci Far-Difference Representations and Gaussian Behavior (with Philippe Demontigny, Thao Do, Archit Kulkarni and Umang Varma), Fibonacci Quarterly (52 (2014), no. 3, 247--273)  pdf
  67. The Pi Mu Epsilon 100th Anniversary Problems: Part II (with James M. Andrews, Avery T. Carr and many of my students), The Pi Mu Epsilon Journal (14 (2013), no. 10, 577--608). pdf
  68. Newman's conjecture in various settings (with Julio Andrade and Alan Chang),  Journal of Number Theory. (144 (2014), 70--91)  pdf
  69. Maass waveforms and low-lying zeroes (with Levent Alpoge, Nadine Amersi, Geoffrey Iyer, Oleg Lazarev and Liyang Zhang), ``Analytic Number Theory: In honor of Helmut Maier's 60th birthday'' (Carl Pomerance, Michael Th. Rassias, editors), Springer-Verlag 2015.  pdf
  70. Generalized Ramanujan Primes (with Nadine Amersi, Olivia Beckwith, Ryan Ronan and Jonathan Sondow). Combinatorial and Additive Number Theory:  CANT 2011 and 2012 (Springer Proceedings in Mathematics & Statistics, Melvyn B. Nathanson editor, 2014, pages 1--13). pdf
  71. Finding and Counting MSTD sets (with Geoffrey Iyer, Oleg Lazarev and Liyang Zhang). Combinatorial and Additive Number Theory:  CANT 2011 and 2012 (Springer Proceedings in Mathematics & Statistics, Melvyn B. Nathanson editor, 2014, pages 79--98).  pdf
  72. Most Subsets are Balanced in Finite Groups (with Kevin Vissuet), Combinatorial and Additive Number Theory:  CANT 2011 and 2012 (Springer Proceedings in Mathematics & Statistics, Melvyn B. Nathanson editor, 2014, pages 147--157)  pdf
  73. Gaussian Behavior in Generalized Zeckendorf Decompositions (with Yinghui Wang), Combinatorial and Additive Number Theory:  CANT 2011 and 2012 (Springer Proceedings in Mathematics & Statistics, Melvyn B. Nathanson editor, 2014, pages 159--173).   pdf
  74. The Pi Mu Epsilon 100th Anniversary Problems: Part III (with many of my students), The Pi Mu Epsilon Journal (14 (2014), no. 1, 65--99). pdf  
  75. Continued Fraction Digit Averages and Maclaurin's Inequalities (with Francesco Cellarosi, Doug Hensley and Jake Wellens), Experimental Mathematics (24 (2015), no. 1, 23--44)  pdf
  76. The \(n\)-Level Density of Dirichlet \(L\)-Functions over \(\mathbb{F}_q[T]\) (with Julio Andrade, Kyle Pratt and Minh-Tam Trinh), Communications in Number Theory and Physics. (8 (2014), no. 3, 511-539)  pdf
  77. The expected eigenvalue distribution of large, weighted \(d\)-regular graphs (with Leo Goldmakher, Cap Khoury and Kesinee Ninsuwan). Random Matrices: Theory and Applications. (3 (2014), no. 2, 1450015, 22 pages)  pdf
  78. The Pi Mu Epsilon 100th Anniversary Problems: Part IV (with many of my students), The Pi Mu Epsilon Journal (15 (2015), no. 2, 100--134) pdf
  79. The James Function (with Christopher N. B. Hammond and Warren P. Johnson),  Mathematics Magazine. (88 (2015), 54--71). pdf
  80. Benford Behavior of Zeckendorf Decompositions (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, C. Turnage-Butterbaugh and M. Weinstein),  Fibonacci Quarterly. (52 (2014), no. 5, 35--46)  pdf
  81. Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald C. Turnage-Butterbaugh and M. Weinstein),  Fibonacci Quarterly. (52 (2014), no. 5, 47--53) pdf
  82. Distribution of eigenvalues of weighted, structured matrix ensembles (with Olivia Beckwith, Victor Luo, Karen Shen and Nicholas Triantafillou), INTEGERS.  (15 (2015), paper A21, 28 pages) pdf 
  83. Limiting Spectral Measures for Random Matrix Ensembles with a Polynomial Link Function (with Kirk Swanson, Kimsy Tor and Karl Winsor), Random Matrices: Theory and Applications (4 (2015), no. 2, 1550004, 28 pages) pdf
  84. Relieving and Readjusting Pythagoras  (with Victor Luo), By The Numbers -- The Newsletter of the SABR Statistical Analysis Committee. (25 (2015), no. 1, 5-14) pdf  (older, expanded version: pdf)
  85. Sums and Differences of Correlated Random Sets (with Thao Do, Archit Kulkarni, David Moon and Jake Wellens) Journal of Number Theory. (147 (2015), 44--68) pdf
  86. Generalizing Zeckendorf's Theorem: The Kentucky Sequence (with M. Catral, P. Ford, P. Harris and D. Nelson), Fibonacci Quarterly. (52 (2014), no. 5, 68--90)  pdf
  87. Gaps between zeros of GL(2) L-functions (with Owen Barrett, Brian McDonald, Ryan Patrick, Caroline Turnage-Butterbaugh and Karl Winsor), Journal of Mathematical Analysis and Applications.  (429 (2015), 204--232) pdf
  88. Surpassing the Ratios Conjecture in the 1-level density of Dirichlet L-functions (with Daniel Fiorilli), Algebra & Number Theory  (9 (2015), no. 1, 13--52) pdf (expanded arXiv version)
  89. Gaps between summands in generalized Zeckendorf decompositions  (with Amanda Bower, Rachel Insoft, Shiyu Li and Philip Tosteson, and an appendix with Iddo Ben-Ari), Journal of Combinatorial Theory, Series A. (135 (2015), 130--160) pdf
  90. Sets Characterized by Missing Sums and Differences in Dilating Polytopes (with Thao Do, Archit Kulkarni, David Moon and Jake Wellens), Journal of Number Theory. (157 (2015), 123--153) pdf
  91. Newman's Conjecture in Function Fields (with Alan Chang, David Mehrle, Tomer Reiter, Joseph Stahl and Dylan Yott), Journal of Number Theory. (15 (2015), 154--169) pdf
  92. Equipartitions and a Distribution for Numbers: A Statistical Model for Benford's Law (with Joe Iafrate and Frederick Strauch), Physical Review E (91 (2015), no. 6, 062138 (6 pages))   pdf
  93. Lower-Order Biases in Elliptic Curve Fourier Coefficients in Families (with Blake Mackall, Christina Rapti and Karl Winsor), Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures (David Kohel and Igor Shparlinski, editors), Contemporary Mathematics 663, AMS, Providence, RI 2016. pdf
  94. From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond (with Owen Barrett, Frank W. K. Firk and Caroline Turnage-Butterbaugh), Open Problems in Mathematics (editors John Nash  Jr. and Michael Th. Rassias, Springer-Verlag, 2016). pdf
  95. Determining Optimal Test Functions for Bounding the Average Rank in Families of L-Functions} (with Jesse Freeman), in SCHOLAR -- a Scientific Celebration Highlighting Open Lines of Arithmetic Research, Conference in Honour of M. Ram Murty's Mathematical Legacy on his 60th Birthday (A. C. Cojocaru, C. David and F. Pappaardi, editors), Contemporary Mathematics 655, AMS and CRM, 2015.. pdf
  96. The Weibull distribution and Benford's Law (with Victoria Cuff and Allie Lewis), Involve (8-5 (2015), 859--874. DOI 10.2140/involve.2015.8.859).  pdf
  97. Some Results in the Theory of Low-lying Zeros (with Blake Mackall, Christina Rapti, Caroline Turnage-Butterbaugh and Karl Winsor, and an appendix with Megumi Asada, Eva Fourakis, Kevin Yang), in Families of automorphic forms and the trace formula (editors), Simons Symposia series, Springer-Verlag. pdf
  98. Leading Digit Laws on Linear Lie Groups (with Corey Manack), Research in Number Theory (1:22  (2015), DOI 10.1007/s40993-015-0024-4).  pdf
  99. Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals  (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald C. Turnage-Butterbaugh and M. Weinstein), INTEGERS (16 (2016), #A6) pdf
  100. Crescent configurations (with David Burt, Eli Goldstein, Sarah Manski, Eyvindur Ari Palsson and Hong Suh), Integers (electronic journal of combinatorial number theory) (16 (2016), #A38)    pdf
  101. Multiple Regression Analysis: Understanding the Impact of Offensive and Defensive Contributions to Team Performance (with Kevin D. Dayaratna),  The Hockey Research Journal (2014/2015, 41--43).   pdf
  102. A Probabilistic Approach to Generalized Zeckendorf Decompositions (with Iddo Ben-Ari), SIAM Journal on Discrete Mathematics (30 (2016), no. 2, 1302--1332) pdf  (journal version here)
  103. Individual Gap Measures from Generalized Zeckendorf Decompositions (with Robert Dorward, Pari Ford, Eva Fourakis, Pamela Harris, Eyvindur Palsson, and Hannah Paugh), Uniform Distribution Theory (12,(2017), no. 1, 27--36). pdf
  104. A Generalization of Zeckendorf's Theorem via Circumscribed m-gons (with Robert Dorward, Pari L. Ford, Eva Fourakis, Pamela E. Harris, Eyvindur A. Palsson and Hannah Paugh), to appear in Involve. pdf
  105. Geometric-Progression-Free Sets over Quadratic Number Fields (with Andrew Best, Karen Huan, Nathan McNew, Jasmine Powell, Kimsy Tor and Madeleine Weinstein), Proceedings of the Royal Society of Edinburgh, Section A: Mathematics (147 (2017), no. 2, 242-262).  pdf
  106. The M&M Game: From Morsels to Modern Mathematics (with Ivan Badinski, Nathan McCue, Cameron Miller, Kayla Miller and Michael Stone). Mathematics Magazine (90 (2017), no. 3, 197--207)  pdf (pruned published version: pdf: Copyright [2017] Mathematical Association of America. All Rights Reserved.).
  107. Legal Decompositions Arising from Non-positive Linear Recurrences (with Minerva Catral, Pari Ford, Pamela Harris, Steven J. Miller, Dawn Nelson), Fibonacci Quarterly  (54 (2016), no. 4, 348--365).  pdf (journal version: pdf)
  108. Subsets of \(\mathbb{F}_q[x]\) Free of 3-term Geometric Progressions (with Megumi Asada, Eva Fourakis, Sarah Manski, Gwyneth Moreland and Nathan McNew), Finite Fields and their Applications (44 (2017), 135--147)  pdf
  109. Fringe pairs in generalized MSTD sets (with Megumi Asada, Sarah Manski and Hong Suh), International Journal of Number Theory. (13 (2017), no. 2, 2653--2675) pdf
  110. On Identities of Ruggles, Horadam, Howard, And Young (with Curtis Cooper, Peter J. C. Moses, Murat Sahin, and Thotsaporn Thanatipanonda), the Proceedings of the 17th International Fibonacci Conference, Fibonacci Quarterly (55 (2017), no. 5, 52--65). pdf
  111. A Collection of Central Limit Type Results in Generalized Zeckendorf Decompositions (with Ray Li), Proceedings of the Seventeenth International Conference on Fibonacci Numbers and Their Applications, Fibonacci Quarterly (55 (2017), no. 5, 105--114).  pdf
  112. On the Asymptotic Behavior of Variance of PLRS Decompositions (with Dawn Nelson, Zhao Pan and Huanzhong Xu), the Proceedings of the 17th International Fibonacci Conference, Fibonacci Quarterly (55 (2017), no. 5, 135--143).  pdf
  113. If a prime divides a product (with Cesar Silva), College Mathematics Journal. (48 (2017), no. 2, 123--128)   pdf
  114. New Behavior in Legal Decompositions Arising from Non-positive Linear Recurrences (with Minerva Catral, Pari Ford, Pamela Harris, Steven J. Miller, Dawn Nelson, Zhao Pan and Huanzhong Xu), Fibonacci Quarterly (55 (2017), no. 3, 252--275). pdf
  115. The Emergence of 4-Cycles in Polynomial Maps over the Extended Integers (with Andrew Best, Patrick Dynes, Jasmine Powell and Ben Weiss, Minnesota Journal of Undergraduate Mathematics. (2 (2016-2017), no. 1, 15 pages) pdf
  116. Low-lying zeros for L-functions associated to Hilbert modular forms of large level) (with Sheng-Chi Liu), Acta Arithmetica (180 (2017), 251--266)  pdf
  117. Constructing families of moderate-rank elliptic curves over number fields (with David Mehrle, Tomer Reiter, Joseph Stahl and Dylan Yott), Minnesota Journal of Undergraduate Mathematics (2 (2016-2017), 11 pages)  pdf
  118. Benford Behavior of Generalized Zeckendorf Decompositions  (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald C. Turnage-Butterbaugh and M. Weinstein), Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer, New York, 2017. pdf
  119. Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions (with Andrew Best, Karen Huan, Nathan Mcnew, Steven J. Miller, Jasmine Powell, Kimsy Tor and Madeleine Weinstein), Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer, New York, 2017. pdf
  120. One-Level density for holomorphic cusp forms of arbitrary level (with Owen Barrett, Paula Burkhardt, Robert Dorward and Jon DeWitt), Research in Number Theory  (3 (2017), no. 25, DOI 10.1007/s40993-017-0091-9) pdf  
  121. Dimensional lower bounds for Falconer type incidence and point configuration theorems (with Jonathan DeWitt, Kevin Ford, Eli Goldstein, Gwyneth Moreland, Eyvindur A. Palsson, Steven Senger), Journal d'Analyse Mathematique.  (139 (2019), 143-154)  pdf
  122. Irrationality measure and lower bounds for \(\pi(x)\) (with David Burt, Sam Donow, Matthew Schiffman and Ben Wieland), The Pi Mu Epsilon Journal (14 (2017), no. 7, 421-429) pdf
  123. When almost all sets are difference dominated in \(\mathbb{Z}/n\mathbb{Z}\) (with Anand Hemmady and Adam Lott), INTEGERS. (17 (2017), Paper No. A54, 15 pp.).  pdf
  124. On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy (with Oscar Gonzalez, Chung Hang Kwan, Roger Van Peski and Tian An Wong), Journal of Number Theory (183 (2018), 407--427).    pdf
  125. Optimal point sets determining few distinct triangles (with Alyssa Epstein, Adam Lott and Eyvindur Palsson), INTEGERS. (18 (2018), Paper No. A16, 17 pp.).    pdf
  126. Benford's Law and Continuous Dependent Random Variables (with Thealexa Becker, David Burt, Taylor C. Corcoran, Alec Greaves-Tunnell, Joseph R. Iafrate, Joy Jing, Jaclyn D. Porfilio, Ryan Ronan, Jirapat Samranvedhya, Blaine Talbut and Frederick W. Strauch), (388 (2018), 350--381) Annals of Physics. pdf.
  127. Random Matrix Ensembles with Split Limiting Behavior (with Paula Burkhardt, Peter Cohen, Jonathan Dewitt, Max Hlavacek, Carsten Sprunger, Yen Nhi Truong Vu, Roger Van Peski, and Kevin Yang, and an appendix joint with  Manuel Fernandez and Nicholas Sieger), Random Matrices: Theory and Applications (7 (2018), no. 3, 39 pages, DOI: 10.1142/S2010326318500065) pdf
  128. Spectral Statistics of Non-Hermitian Random Matrix Ensembles (with Ryan Chen, Yujin Kim, Jared Lichtman, Shannon Sweitzer, and Eric Winsor), Random Matrices: Theory and Applications  (8 (2019), no. 1, 40 pages) pdf
  129. The bidirectional ballot polytope (with Carsten Peterson, Carsten Sprunger and Roger Van Peski),  INTEGERS (81 (2018), #A81, 1--18) pdf
  130. On Summand Minimality of Generalized Zeckendorf Decompositions (with Katherine Cordwell, Max Hlavacek, Chi Huynh, Carsten Peterson, and Yen Nhi Truong Vu), Research in Number Theory  (4 (2018), no. 43, https://doi.org/10.1007/s40993-018-0137-7) pdf
  131. When Sets Can and Cannot Have MSTD Subsets (with Hung Chu, Nathan McNew, Victor Xu and Sean Zhang).  Journal of Integer Sequences. (21 (2018), Article 18.8.2: https://cs.uwaterloo.ca/journals/JIS/VOL21/Miller/miller8.pdf)
  132. Book Review: F. Dyson: Maker of Patterns (An Autobiography Through Letters), Liveright, 2018, 416 pages, book review for the Notices of the American Mathematical Society (66 (May 2019, no. 5, 750--753).  pdf or pdf
  133. On algorithms to calculate integer complexity (with Katherine Cordwell, Alyssa Epstein, Anand Hemmady, Eyvindur A. Palsson, Aaditya Sharma, Stefan Steinerberger, Yen Nhi Truong Vu), INTEGERS. (19 (2019), A12, 13 pages) pdf
  134. Limiting Distributions in Generalized Zeckendorf Decompositions (with Alex Gueganic, Granger Carty, Yujin H. Kim, Alina Shubina, Shannon Sweitzer, Eric Winsor and Jianing Yang), Fibonacci Quarterly. (57 (2019), no. 2, 109--125) pdf
  135. Gaussian Behavior in Zeckendorf Decompositions From Lattices (with Eric Chen, Robin Chen, Lucy Guo, Cindy Jiang, Joshua M. Siktar, Peter Yu), Fibonacci Quarterly. (57 (2019), no. 3, 201--212) pdf
  136. Central Limit Theorems for Gaps of Generalized Zeckendorf Decompositions (with Ray Li), Fibonacci Quarterly. (57 (2019), no. 3, 213--230)  pdf
  137. The Zeckendorf Game (with Paul Baird-Smith, Alyssa Epstein and Kristen Flint), Proceedings of CANT 2018.  pdf
  138. A geometric perspective on the MSTD question (with Carsten Peterson), Discrete and Computational Geometry. (62 (2019), no. 4, 832-855): https://doi.org/10.1007/s00454-019-00109-7)  pdf
  139. Upper Level Mathematics and Statistics Courses Shared Across Campuses (with Stephan Ramon Garcia and Jingchen Hu), to appear in Teaching and Learning Mathematics Online.   pdf
  140. Generalizations of a Curious Family of MSTD Sets Hidden By Interior Blocks (with Hung Chu, Noah Luntzlara and Lily Shao) INTEGERS.  (20A (2020), #A5)  pdf
  141. Gaps of Summands of the Zeckendorf Lattice (with Neelima Borade, Dexter Cai, David Z. Chang, Bruce Fang, Alex Liang and Wanqiao Xu), Fibonacci Quarterly. (2 (2020), 143-156),  pdf
  142. Infinite Families of Partitions into MSTD Subsets (with Hung Chu, Noah Luntzlara and Lily Shao), INTEGERS. (19 (2019), #A60)  pdf
  143. On Near Perfect Numbers (with Peter Cohen, Katherine Cordwell, Alyssa Epstein, Chung Hang Kwan and Adam Lott) Acta Arithmetica. (194 (2020), no. 4, 341-366)  pdf
  144. The Generalized Zeckendorf Game (with Paul Baird-Smith, Alyssa Epstein and Kristen Flint), Fibonacci Quarterly (57 (2019) no. 5, 1-14)  pdf
  145. Benford's Law Beyond Independence: Tracking Benford Behavior in Copula Models (with Becky Durst). Involve (19 (2020), no. 7, 1193-1218) pdf
  146. The Fibonacci Quilt Game (with Alexandra Newlon), Fibonacci Quarterly (2 (2020), 157-168) pdf
  147. Upper Level Mathematics and Statistics Courses Shared Across Campuses (with Stephan Garcia and Jingchen (Monika) Hu), contributed chapter in ``Teaching and Learning Mathematics Online'', James P. Howard II and John F. Beyers (editors), Chapman and Hall/CRC, Boca Raton, Florida, 2020. pdf
  148. Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics (with Sara Fish and Dylan King), Bulletin of the Australian Mathematical Society (2020, 1--11, doi:10.1017/S000497272000026X). pdf
  149. Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice (with Evan Fang, Jonathan Jenkins, Zack Lee, Daniel Li, Ethan Lu, Dilhan Salgado, Joshua Siktar),  Fibonacci Quarterly. (3 (2020), 208-225)   pdf

  150. Higher Order Fibonacci Sequences from Generalized Schreier sets (with Hung Viet Chu, Zimu Xiang), Fibonacci Quarterly. (3 (2020), 249-253)  pdf

  151. Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture} (with Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon, Alvaro Lozano-Robledo). Journal of Number Theory (215 (2020), 339-361)  pdf (arxiv)  or pdf
  152. The Inverse Gamma Distribution and Benford's Law (with Rebecca F. Durst, Chi Huynh, Adam Lott, Eyvindur A. Palsson, Wouter Touw, and Gert Vriend), The PUMP Journal of Undergraduate Research (3 (2020), 95-109).   pdf
  153. On the sum of k-th powers in terms of earlier sums (with Enrique Trevino), the College Mathematics Journal. (48 (2020), no. 2, 123--128)   (arxiv version: pdf)
  154. Recurrence Relations and Benford's Law (with Madeleine Farris, Noal Luntzlara, Lily Shao and Mengxi Lang), Statistical Methods and Applications. (30 (2021), 797-817: DOI: https://doi.org/10.1007/s10260-020-00547-1) pdf
  155. Distribution of missing differences in diffsets (with Scott Harvey-Arnold and Fei Peng), Combinatorial and Additive Number Theory IV, Springer-Verlag (2021), 261--281. pdf
  156. Extending Zeckendorf's Theorem to a Non-constant Recurrence and the Zeckendorf Game on this Non-constant Recurrence Relation (with Ela Boldyriew, Anna Cusenza, Linglong Dai, Pei Ding, Aidan Dunkelberg, John Haviland, Kate Huffman, Dianhui Ke, Daniel Kleber, Jason Kuretski, John Lentfer, Tianhao Luo, Clayton Mizgerd, Vashisth Tiwari, Jingkai Ye, Yunhao Zhang, Xiaoyan Zheng, and Weiduo Zhu), Fibonacci Quarterly. (5 (2020), 55-76)  pdf
  157. Deterministic Zeckendorf Games (with Ruoci Li, Xiaonan Li, Clay Mizgerd, Chenyang Sun, Dong Xia, And Zhyi Zhou), Fibonacci Quarterly. (58 (2020), no. 5, 152-160)  p3df
  158. Winning Strategy for the Multiplayer and Multialliance Zeckendorf Games (with Anna Cusenza, Aiden Dunkelberg, Kate Huffman, Dianhui Ke, Daniel Kleber, Clayton Mizgerd, Vashisth Tiwari, Jingkai Ye, Xiaoyan Zheng), Fibonacci Quarterly. (59 (2021), 308--318)  pdf
  159. Crescent Configurations in Normed Spaces (with Sara Fish, Dylan King, Eyvi Palsson and Catherine Wahlenmayer), INTEGERS.  (20 (2020), #A96)  pdf  (lot of files, use .zip instead of .tex to get source)
  160. An Introduction to Completeness of Positive Linear Recurrence Sequences (with Ela Boldyriew, John Haviland, Phuc Lam, John Lentfer, Fernando Trejos Suarez), Fibonacci Quarterly. (58 (2020), no. 5, 77-90)  pdf 
  161. The Co-Video Mathematician, Math in the Time of Corona, Part of the Mathematics Online First Collections book series (MOFC), Alice Wonders (editor) (2021, 79-86): chapter here   book here.
  162. The Explicit Sato-Tate Conjecture For Primes In Arithmetic Progressions (with Trajan Hammonds, Casimir Kothari, Noah Luntzlara, Jesse Thorner, Hunter Wieman).  IJNT  (17 (2021), no. 8, 1905--1923)   pdf
  163. Lessons from the German Tank Problem (with George Clark and Alex Gonye), Mathematical Intelligencer.  (62 (2021): https://doi.org/10.1007/s00283-021-10082-w) pdf 
  164. Zeckendorf's Theorem Using Indices in an Arithmetic Progression (with Amelia Gilson, Hadley Killen, Tamas Lengyel, Nadia Razek, Joshua M. Siktar, and Liza Sulkin,  Fibonacci Quarterly.  (59 (2021), 327--337) pdf
  165. When Rooks Miss: Probability through Chess (with Daniel Turek, Haoyu Sheng), College Mathematics Journal (52 (2021, no. 2, 84-93) pdf
  166. Generalizing Ruth-Aaron Numbers (with Nancy Jiang), The PUMP Journal of Undergraduate Research (4 (2021), 20-62)  pdf
  167. Lower-Order Biases Second Moments of Dirichlet Coefficients in Families of L-Functions (with Megumi Asada, Ryan Chen, Eva Fourakis, Yujin Kim, Andrew Kwon, Jared Lichtman, Blake Mackall, Eric Winsor, Karl Winsor, Jianing Yang, Kevin Yang; appendix with Roger Weng), to appear in Experimental Mathematics,  pdf
  168. When Life Gives You Lemons, Make Mathematicians (with Kira Adaricheva, Ben Brubaker, Pat Devlin, Steven J. Miller, Vic Reiner, Alexandra Seceleanu, Adam Sheffer, and Yunus Zeytuncu), Notices of the AMS (68 (2021)  no. 3, 375-478). pdf
  169. An Introduction to Completeness of Positive Linear Recurrence Sequences (with Ela Boldyriew, John Haviland, Phuc Lam, John Lentfer, Fernando Trejos Suarez).  Fibonacci Quarterly (5 (2020), 77--90)  pdf 

  170. Constructions of Generalized MSTD Sets in Higher Dimensions (with Elena Kim), Journal of Number Theory  (235 (2022), 358--381) pdf

  171. Biases in Moments of the Dirichlet Coefficients in One-Parameter Families of Elliptic Curves (with Weng (Roger) Yan), The PUMP Journal of Undergraduate Research (4 (2021), 168--201).  pdf
  172. The limiting spectral measure for an ensemble of generalized checkerboard matrices (with Fangu Chen, Yuxin Lin and Jiahui Yu).  The PUMP Journal of Undergraduate Research (4 (2021), 202--221).  pdf
  173. Generalizing the Distribution of Missing Sums in Sumsets (with Hung Chu, Dylan King, Noah Noah Luntzlara, Thomas C. Martinez, Lily Shao, Chenyang Sun, Victor Xu). Journal of Number Theory  (239 (2022), 402--444) pdf
  174. Distinct Angle Problems and Variants (with Henry Fleischmann, Hongyi Hu, Faye Jackson, Ethan Pesikoff, Eyvindur Palsson, Charles Wolf), Discrete & Computational Geometry (2023: https://doi.org/10.1007/s00454-022-00466-w). pdf 
  175. Bounds on Zeckendorf Games (with Anna Cusenza, Aiden Dunkelberg, Kate Huffman, Dianhui Ke, Daniel Kleber, Micah McClatchey, Clayton Mizgerd, Vashisth Tiwari, Jingkai Ye, Xiaoyan Zheng), Fibonacci Quarterly. pdf  (1 (2022), no. 1, 57--71)
  176. Benfordness of the Generalized Gamma Distribution (with Zelong Bi and Irfan Durmic), The PUMP Journal of Undergraduate Research   (5 (2022), 89-104)  pdf  Journal version: pdf
  177. Limiting Spectral Distributions of Families of Block Matrix Ensembles (with Teresa Dunn, Henry Fleischmann, Faye Jackson, Simran Khun, Luke Reifenberg, Alexander Shashkov, Stephen Willis). The PUMP Journal of Undergraduate Research (5 (2022), 122-147) pdf. Journal version: pdf
  178. Modeling Random Walks to Infinity on Primes in $\mathbb{Z}[\sqrt{2}]$ (with Bencheng Li, Tudor Popescu, Daniel Sarnecki and Nawapan Wattanawanichkul), Journal of Integer Sequences (25 (2022), Article 22.6.1).  pdf
  179. On Zeckendorf related partitions using the Lucas sequence (with Hung Viet Chu and David Luo), Fibonacci Quarterly.  (60 (2022), 111--119) pdf (arxiv version: pdf)
  180. k-Diophantine m-tuples in finite fields (with Trajan Hammonds, Seoyoung Kim, Arjun Nigam, Kyle Onghai, Dishant Saikia, Lalit M. Sharma), International Journal of Number Theory (19 (2023), no. 4, 891--912)  pdf
  181. Determining optimal test functions for 2-level densities (with Elzbieta Boldyriew, Fangu Chen, Charles Devlin VI, Jason Zhao). Research in Number Theory (9 (2023), article number 32, https://doi.org/10.1007/s40993-022-00367-0) pdf
  182. A New Benford Test for Clustered Data with Applications to American Elections (Katherine M. Anderson, Kevin Dayaratna, Drew Gonshorowski and Steven J. Miller), in Benford's Law(s) and Applications (special edition of Stats),\textbf{5} (2022), no. 3, 841--855.  pdf
  183. Walking to Infinity on the Fibonacci Sequence (Steven J. Miller, Fei Peng, Tudor Popescu, Nawapan Wattanawanichkul), Fibonacci Quarterly.  (5 (2022), 293--298)  pdf

  184. Bounding Vanishing at the Central Point of Cuspidal Newforms (with Jiahui (Stella) Li), Journal of Number Theory (Computational Section, 244 (March 2023), 279--307)    pdf

  185. On Benford's Law and the Coefficients of the Riemann Mapping Function for the Exterior of the Mandelbrot set, Filippo Beretta, Jesse Dimino, Weike Fang, Thomas C. Martinez, Steven J. Miller, and Daniel Stoll, Fractal and Fractional.  (6 (2022), 534, https://doi.org/10.3390/fractalfract6100534)  pdf
  186. Distinct angles in general position (Henry L. Fleischmann, Sergei V. Konyagin, Steven J. Miller, Eyvindur A. Palsson, Ethan Pesikoff, Charles Wolf), Discrete Mathematics  (346 (2023), no. 4, 113283ac) pdf.
  187. Sums of Reciprocals of Recurrence Relations (with Hao Cui, Xiaoyu Cui, Sophia C. Davis, Irfan Durmi ́C, Qingcheng Hu, Lisa Liu, Fengping Ren, Alicia Smith Reina, and Eliel Sosis), Fibonacci Quarterly.  (Conference Proceedings: 20th International Fibonacci Conference: 60 (2022), no.5, 111--142). pd
  188. The Bergman Game (with Benjamin Baily, Justine Dell, Irfan Durmic, Henry Fleischmann, Faye Jackson, Isaac Mijares, Ethan Pesikoff, Luke Reifenberg, Alicia Smith Reina, Yingzi Yang), Fibonacci Quarterly.  (Conference Proceedings: 20th International Fibonacci Conference: 60 (2022), no.5, 18--38). pdf
  189. Completeness of Positive Linear Recurrence Sequences (with Ela Boldyriew, John Haviland, Phuc Lam, John Lentfer, Fernando Trejos Suarez), CANT V (Springer Proceedings in Math and Statistics 395 (2023), 21-78). pdf 
  190. Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, I (with Thomas Martinez, Clay Mizgerd and Chenyang Sun), Fibonacci Quarterly.  (Conference Proceedings: 20th International Fibonacci Conference: 60 (2022), no.5, 222--230). pdf
  191. Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, II (with Thomas Martinez, Clay Mizgerd, Jack Murphy and Chenyang Sun), Fibonacci Quarterly.  (Conference Proceedings: 20th International Fibonacci Conference: 60 (2022), no.5, 231--254). pdfAn
  192. Winning Strategies for the Generalized Zeckendorf Game (Steven J. Miller, Eliel Sosis, Jingkai Ye), Fibonacci Quarterly.  (Conference Proceedings: 20th International Fibonacci Conference: 60 (2022), no.5, 270--292). pdf
  193. Recurrence relations for S-legal index difference sequences (Guilherme Zeus Dantas E Moura, Andrew Keisling, Astrid Lilly, Annika Mauro, Steven J. Miller, Matthew Phang, and Santiago Velazquez Iannuzzelli),  Fibonacci Quarterly.  (61 (2023), no. 3, 257--274)  pdf
  194. Generalizing the German Tank Problem (Anthony Lee and Steven J. Miller), The PUMP Journal of Undergraduate Research. (6 (2023, 59-95) pdf (journal version here)
  195. Distinct Angles and Angle Chains in Three Dimensions (Ruben Ascoli, Livia Betti, Jacob Lehmann Duke, Xuyan Liu, Wyatt Milgrim, Steven J. Miller, Eyvindur A. Palsson, Francisco Romero Acosta, Santiago Velazquez
    Iannuzzelli),  Discrete Mathematics \& Theoretical Computer Science.  (25 (2023), no. 1, https://doi.org/10.46298/dmtcs.10037)  pdf 
  196. The Accelerated Zeckendorf Game (Diego Garcia-Fernandezsesma, Steven J. Miller, Thomas Rascon, Risa Vandegrift, and Ajmain Yamin), Fibonacci Quarterly (62 (2024), no. 1, 3--14).  pdf
  197. A Refined Conjecture for the Variance of Gaussian Primes Across Sectors) (with Ryan C. Chen, Yujin H. Kim, Jared D. Lichtman, Alina Shubina, Shannon Sweitzer, Ezra Waxman, Eric Winsor, Jianing Yang).  Experimental Mathematics. (published online May 2020; volume 32 (2023), no. 1, 33-53)  pdf
  198. Schreier Multisets and the s-step Fibonacci Sequences (Hung Viet Chu, Nurettin Irmak, Steven J. Miller, Laszlo Szalay and Sindy Xin Zhang), Conference Proceedings of the 2023 Integers Conference  pdf  (De Gruyter 20 DOI: https://doi.org/10.1515/9783111395593-007)
  199. VC-Dimension and Distance Chains in \(\Bbb F}_q^d\) (Ruben Ascoli, Livia Betti, Justin Cheigh, Alex Iosevich, Ryan Jeong, Xuyan Liu, Brian McDonald, Wyatt Milgrim, Steven J. Miller, Francisco Romero Acosta, Santiago Velazquez Iannuzzelli), Korean Journal of Mathematics.  (32 (2024), no. 1, 43--57) pdf
  200. Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triple (with Thomas Jaklitsch, Thomas Martinez and Sagnik Mukherjee). to appear in the Rocky Mountain Journal of Mathematics  pdf
  201. Optimal Point Sets Determining Few Distinct Angles (Henry L. Fleischmann, Steven J. Miller, Eyvindur A. Palsson, Ethan Pesikoff, Charles Wolf),  The Australasian Journal of Combinatorics (87 (2023), no. 1, 165--181) pdf
  202. Extending the support of 1- and 2-level densities for cusp form L-functions under square-root cancellation hypotheses (Annika Mauro, Jack Miller, and Steven J. Miller), to appear in Acta Arithmetica, Special Issue in honor of Henryk Iwaniec's 75th birthday. pdf 
  203. GOATs and BOATs; or When Might 11/13 be Less Than 6/18?  (with Rick Cleary), Mathematics and Sports, (5 (2023), no. 1)  pdf
  204. The Reversed Zeckendorf Game (Zoe Batterman, Aditya Jambhale, Steven J. Miller, Akash L. Narayanan, Kishan Sharma, Andrew Yang, and Chris Yao), to appear in the 21st International Fibonacci Conference Proceedings.  pdf
  205. Investigations in Patterns in Last Digits of Square Numbers and Higher Powers (Steven J. Miller, Elizabeth Wiley and Julia Wiley), The PUMP Journal of Undergraduate Research.  (7 (2024), 14-28)  pdf   
  206. Applications of Moments of Dirichlet Coefficients in Elliptic Curve Families (Zoe Batterman, Aditya Jambhale, Steven J. Miller, Akash L. Narayanan, Kishan Sharma, Andrew Yang, Chris Yao), International Journal of Data Science in the Mathematical Sciences (Special Issue on ICERM: Murmurations in Arithmetic, Guest Editors Yang-Hui He, Kyu-Hwan Lee and Thomas Oliver), (2 (2024), No. 02, 99--113).  pdf
  207. Sums of Powers of Primes in Arithmetic Progression (Muhammet Boran, John Byun, Zhangze Li, Steven J. Miller, and Stephanie Reyes), The PUMP Journal of Undergraduate Research. (7 (2004), 29--50) pdf
  208. A survey of a random matrix model for a family of cusp forms (Owen Barrett, Zoe X. Batterman, Aditya Jambhale, Steven J. Miller, Akash L. Narayanan, Kishan Sharma, Chris Yao), to appear in ``Essays in Analytic Number Theory -- In Honor of Helmut Maier's 70th Birthday'' (John Friedlander, Carl Pomerance, and Michael Th. Trassias, editors). pdf 
  209. Linear Recurrences of Order at Most Two in Nontrivial Small Divisors and Large Divisors (Hung Viet Chu, Kevin Huu Le, Steven J. Miller, Yuan Qiu, and Liyang Shen), to appear in Combinatorial and Additive Number Theory 2022 & 2023, CANT VI (Melvyn B. Nathanson, editor), Springer Proceedings in Mathematics \& Statistics.  pdf  
  210. Towards the Gaussianity of Random Zeckendorf Games (Justin Cheigh, Guilherme Zeus Dantas E Moura, Ryan Jeong, Jacob Lehmann Duke, Wyatt Milgrim, Steven J. Miller, and Prakod Ngamlamai), to appear in the CANT 2022 and 2023 Proceedings.    pdf
  211. Linear Recurrences of Order at Most Two in Nontrivial Small Divisors and Large Divisors (Hung Viet Chu, Kevin Huu Le, Steven J. Miller, Yuan Qiu, and Liyang Shen), to appear in the  Combinatorial and Additive Number Theory Proceedings 2022 and 2023, CANT VI (Melvyn B. Nathanson, editor), Springer Proceedings in Mathematics \& Statistics.   pdf
  212. Applications of Improvements to the Pythagorean Won-Loss Expectation in Optimizing Rosters (Alexander Almeida, Kevin Dayaratna, Steven J. Miller and Andrew Yang), book chapter to appear in Artificial Intelligence, Optimization, and Data Sciences in Sports, Springer Optimization and its Applications series.  pdf  (zipped file of code and related files here)
  213. Sum and Difference Sets in Generalized Dihedral Groups (Ruben Ascoli, Justin Cheigh, Guilherme~Zeus Dantas~e~Moura, Ryan Jeong, Andrew Keisling, Astrid Lilly, Steven J. Miller, Prakod Ngamlamai, Matthew Phang), to appear in the Proceedings of the 34th Midwestern Conference on Combinatorics and Combinatorial Computing (MCCCC34).  pdf
  214. Generalized Continuous and Discrete Stick Fragmentation and Benford's Law (Xinyu Fang, Steven J. Miller, Maxwell Sun, Amanda Verga), to appear in the Journal of Number Theory.  pdf
  215. Extending support for the centered moments of the low lying zeroes of cuspidal newforms (Peter Cohen, Justine Dell, Oscar E. Gonzalez, Geoffrey Iyer, Simran Khunger, Chung-Hang Kwan, Steven J. Miller, Alexander Shashkov, Alicia Smith Reina, Carsten Sprunger, Nicholas Triantafillou, Nhi Truong, Roger Van Peski, Stephen Willis, and Yingzi Yang), to appear in Algebra & Number Theory.  pdf 
  216. Walking to Infinity Along Some Number Theory sequences (with Fei Peng, Tudor Popescu, Joshua M. Siktar, Nawapan Wattanawanichkul, and the Polymath REU Program), Integers.  pdf
  217. On the Within-Perfect Numbers (Chung-Hang Kwan and Steven J. Miller), to appear in the Quarterly Journal of Mathematics.   pdf
  218. $v$-Palindromes: An Analogy To The Palindromes (Chris Bispels, Muhammet Boran, Steven J. Miller, Eliel Sosis, and Daniel Tsai), The PUMP Journal of Undergraduate Research. (7 (2024), 186--206)  pdf
  219. Sums of Powers by L'Hopital's Rule (Eduardo Duenez, Asimina S. Hamakiotes and Steven J. Miller), to appear in the Fibonacci Quarterly pdf

  220. Bounding Excess Rank of Cuspidal Newforms via Centered Moments (Sohom Dutta, Steven J. Miller). Research in Number Theory (10 (2024), no. 76: https://doi.org/10.1007/s40993-024-00567-w) pdf

  221. Avoiding 3-Term Geometric Progressions in Non-Commutative Settings (with Megumi Asada, Bruce Fang, Eva Fourakis, Sarah Manski, Nathan McNew, Gwyneth Moreland, Ajmain Yamin, Sindy Xin Zhang), Journal of Integer Sequences. pdf   (27 (2024), Article 24.7.7: https://cs.uwaterloo.ca/journals/JIS/VOL27/McNew/mcnew6a.html)
  222. The German Tank Problem with Multiple Factories (Steven J. Miller, Kishan Sharma, Andrew Yang), The PUMP Journal of Undergraduate Research  (7 (2024), 231--257). pdf
  223. Benford's Law under Zeckendorf Decomposition (Sungkon Chang, Steven J. Miller), to appear in the 21st International Fibonacci Conference Proceedings.  pdf
  224. An Invitation to Fibonacci Digits (Justin Cheigh, Guilherme Zeus Dantas e Moura, Jacob Lehmann Duke, Annika Mauro, Zoe McDonald, Anna Mello, Kayla Miller, Steven J. Miller, Santiago Velazquez Iannuzzelli), to appear in the Fibonacci Quarterly. pdf
  225. Nature by Numbers (Steven J. Miller, Crist$\acute{{\rm o}}$bal Vila and Iana Vranesko), to appear in the Fibonacci Quarterly.   pdf
  226. A Pair of Diophantine Equations Involving the Fibonacci Numbers (Xuyuan Chen, Hung Viet T Chu, Fadhlannafis K. Kesumajana, Dongho Kim, Liran Li, Steven J. Miller, Junchi Yang, and Chris Yao).  To appear in the Fibonacci Quarterly.   pdf
  227. Problem Session Notes from CANT Conferences (currently 2009 through 2016, inclusive); distributed to interested parties and posted on the arXiv, 35 pages. pdf

SUBMITTED  PAPERS   

  1. Classification of crescent configurations (with Rebecca F. Durst, Max Hlavacek, Chi Huynh, Steven J. Miller and Eyvindur A. Palsson), submitted to INTEGERS.   pdf

  2. Distribution of Eigenvalues of Random Real Symmetric Block Matrices (with Keller Blackwell, Neelima Borade, Charles Devlin VI, Noah Luntzlara, Renyuan Ma, Mengxi Wang, Wanqiao Xu), Submitted August 2019 to Random Matrices: Theory and Applications. Expanded arXiv version: pdf. Paper revised with Arup Bose and Soumendu Sundar Mukherjee, retitled Distribution of Eigenvalues of Matrix Ensembles arising from Wigner and Palindromic Toeplitz Blocks, submitted to Random Matrices: Theory and Applications.  pdf

  3. Tinkering with Lattices: A New Take on the Erdos Distance Problem (with E. Boldyriew, E. Kim, E. Palsson, S. Sovine, F. Trejos Suarez and J. Zhao), submitted to Integers (electronic journal of combinatorial number theory).  pdf

  4. The Generalized Bergman Game (with Benjamin Baily, Justine Dell, Irfan Durmic, Henry Fleischmann, Faye Jackson, Isaac Mijares, Ethan Pesikoff, Luke Reifenberg, Alicia Smith Reina, Yingzi Yang), submitted to the Fibonacci Quarterly. pdf  (arXiv link: https://arxiv.org/abs/2109.00117)

  5. Class Numbers and Pell's Equation x^2 + 105y^2 = z^2 (with Thomas Jaklitsch, Thomas Martinez and Sagnik Mukherjee). Submitted to Proceedings of ICCGNFRT - 2021 pdf
  6. Irreducibility Over the Max-Min Semiring (with Ben Baily, Justine Dell, Henry L. Fleishschmann, Faye Jackson, Ethan Pesikoff, Luke Reifenberg). Submitted to the Journal of Integer Sequences   pdf
  7. The Real Schwarz Lemma: The Sequel (with Ben Baily, Jonathan Geller). Submitted to    pdf
  8. Virus Dynamics on k-Level Starlike Graphs (Aki Takigawa and Steven J. Miller).  pdf
  9. Sum and Difference Sets in Generalized Dihedral Groups (Ruben Ascoli, Justin Cheigh, Guilherme Zeus Dantas e Moura, Ryan Jeong, Andrew Keisling, Astrid Lilly, Steven J. Miller, Prakod Ngamlamai, Matthew Phang), submitted December 2022 to the Proceedings of the 34th Midwestern Conference on Combinatorics and Combinatorial Computing (MCCCC34).  pdf
  10. Indecomposability Over the Max-Min Semiring (Benjamin Baily, Justine Dell, Henry L. Fleischmann, Faye Jackson, Steven J. Miller, and Ethan Pesikoff), submitted to the Journal of Integer Sequences    pdf
  11. Benfordness of measurements resulting from box fragmentation (Livia Betti, Irfan Durmic, Zoe Mcdonald, Jack B. Miller and Steven J. Miller), submitted to the Journal of Statistical Theory and Practice (the AISC 2022 issue).   pdf
  12. A characterization of prime $v$-palindromes (Muhammet Boran, Garam Choi, Steven J. Miller, Jesse Purice and Daniel Tsai), submitted to the CANT proceedings. pdf
  13. VC-Dimension of Hyperplanes over Finite Fields (Ruben Ascoli, Livia Betti, Justin Cheigh, Alex Iosevich, Ryan Jeong, Xuyan Liu, Brian McDonald, Wyatt Milgrim, Steven J. Miller, Francisco Romero Acosta, Santiago Velazquez Iannuzzelli), submitted to Graphs and Combinatorics  pdf
  14. Benford behavior of a higher dimensional fragmentation process (Irfan Durmic, Steven J. Miller), submitted to The PUMP Journal of Undergraduate Research. pdf
  15. On a pair of Diophantine Equations (S. Uthsara, K. Arachchi, H. V. Chu, J. Liu, Q. Luan, R. Marasinghe, and S. J. Miller), submitted to CANT 2024.   pdf
  16. Phase Transitions for Binomial Sets Under Linear Forms (Ryan Jeong, Steven J. Miller), submitted to Combinatorics, Probability and Computing  pdf
  17. Limiting Behavior in Missing Sums of Sumsets (Aditya Jambhale, Rauan Kaldybayev, Steven J. Miller, Chris Yao), submitted to CANT 2024. pdf
  18. Extending James' Pythagorean Formula for Head-to-Head Matchups (R. Cleary, J. Jeffries, C. Miller, S. J. Miller, J. Murray, N. Skiera), submitted to the Journal of Sports Analytics.   pdf

  19. Upper Bounds for the Lowest First Zero in Families of Cuspidal Newforms (Palak Arora, Glenn Bruda, Bruce Fang, Raul Marquez, Steven J. Miller, Beni Prapashtica, Vismay Sharan, Daeyoung Son, Xueyiming Tang and Saad Waheed), submitted to Journal of Number Theory.  pdf

  20. On a Pair of Diophantine Equations (Sujith Uthsara Kalansuriya Arachchi, Hung Videt Chu, Jiasen Liu, Qitong Luan, Rukshan Marasinghe, and Steven J. Miller), submitted to the 2024 CANT Proceedings.   pdf
  21. Sum of Consecutive Terms of Pell and Related Sequences (Navvye Anand, Amit Kumar Basistha, Kenny B. Davenport, Alexander Gong, Steven J. Miller, Alexander Zhu), submitted to the Conference Proceedings of the 21st International Fibonacci conference.   pdf
  22. Effect of the Weight on the Excised Model for Quadratic Families of L-Functions (Owen Barrett, Zoe X. Batterman, Aditya Jambhale, Steven J. Miller, Akash L. Narayanan, Kishan Sharma, Chris Yao), pdf
  23. Extending James' Pythagorean Formula For Head-To-Head Matchups (Richard Cleary, Jake Jeffries, Cameron Miller, Steven J. Miller, James Murray, and Nick Skiera)  pdf
  24. wSLG: Redefining the Relative Values of Various Hits in Baseball (Alex Cardonick, Mac Carso, Rick Cleary, Jacob Eckerle, S. J. Miller, Ethan Prout and Evan Ruschil)  pdf
  25. Sums of Powers by L'Hopital's Rule (Eduardo Duenez, Asimina S. Hamakiotes and Steven J. Miller), submitted to the Fibonacci Quarterly. pdf 

  26. Variants of Conway Checkers and k-nacci Jumping (Glenn Bruda, Joseph Cooper, Kareem Jaber, Raul Marquez and Steven J. Miller), submitted to the Fibonacci Quarterly (special issue in honor of Peter G. Anderson, Marjorie Bicknell-Johnson and William Webb) pdf

  27. On the Density of Low Lying Zeros of a Large Family of Automorphic L-Functions (Timothy Cheek, Pico Gilman, Kareem Jaber, Steven J. Miller, and Marie-Helene Tome), Research in Number Theory.  pdf

  28. Stability Of Matrix Recurrence Relations (Glenn Bruda, Bruce Fang, Pico Gilman, Raul Marquez, Steven J. Miller, Beni Prapashtica, Daeyoung Son, Saad Waheed, Janine Wang), submitted to the Fibonacci Quarterly. pdf

  29. A Random Matrix Model for a Family of Cusp Forms (Owen Barrett, Zoe Batterman, Aditya Jambhale, Steven J. Miller, Akash Narayanan, Kishan Sharma, Chris Yao), submitted September 2024 to Experimental Mathematics.    pdf

  30. Black Hole Zeckendorf Games (Caroline Cashman, Steven J. Miller, Jenna Shuffelton, Daeyoung Son), submitted to the Fibonacci Quarterly (special issue in honor of Peter G. Anderson, Marjorie Bicknell-Johnson and William Webb). pdf

  31. Numerical Investigation of Lower Order Biases in Moment Expansions of One Parameter Families of Elliptic Curves (Timothy Cheek, Pico Gilman, Kareem Jaber, Steven J. Miller, Marie-Helene Tome). Journal of Number Theory    pdf

  32. Optimal Doubling Thresholds in Backgammon-like Stochastic Games (Haoru Ju, Daniel Leifer, Steven J. Miller, Sooraj A. Padmanabhan, Chenyang Sun, Luke Tichi, Benjamin Tocher, and Kiley Wallace), Fibonacci Quarterly (special issue in honor of Art Benjamin and Curtis Cooper). pdf
  33. Dynamics of the Fibonacci Order of Appearance Map (Molly FitzGibbons, Steven J. Miller, Amanda Verga), submitted to the Fibonacci Quarterly (special issue in honor of Art Benjamin and Curtis Cooper).  pdf
  34. Hyper-bishops, Hyper-rooks, and Hyper-queens: Percentage of Safe Squares on Higher Dimensional Chess Boards (Caroline Cashman, Joseph Cooper, Raul Marquez, Steven J. Miller, Jenna Shuffleton),  Mathematics Magazine  pdf
  35. Composite Numbers in an Arithmetic Progression (Hung Viet Chu, Steven J. Miller, Joshua Siktar), submitted to Mathematics Magazine.  pdf
  36. Survey Article on: Numerical Investigation of Lower Order Biases in Moment Expansions of One Parameter Families of Elliptic Curves (Timothy Cheek, Pico Gilma, Kareem Jaber, Steven J. Miller, Vismay Sharan, Marie-Helene Tome), to be submitted to the Conference Proceedings of the Stony Brook Murmurations Meeting (Fall 2024).

  37. Leslie Population Models in Predator-prey and Competitive populations: theory and applications by machine learning (Pico Gilman, Steven J. Miller, Daeyoung Son, Saad Waheed, Janine Wang).   pdf

  38. Sum of Consecutive Terms of Pell and Related Sequences (Navvye Anand, Amit Kumar Basistha, Kenny B. Davenport, Alexander Gong, Florian Luca, Steven J. Miller, Alexander Zhu), submitted to the Fibonacci Quarterly (January 2025).   pdf
     

PREPRINTS / IN  PREPARATION (available upon request)   

  1. The Ratios Conjecture and Convolving Families of \(L\)-functions (with Minh-Tam Trinh).
  2. When Generalized Sumsets are Difference Dominated (with Virginia Hogan). pdf
  3. Moment Formulas for Ensembles of Classical Compact Groups (with Geoffrey Iyer and Nicholas Triantafillou)
  4. \(m\)-Paths and the \(3x+1\) Problem (with Bruce Adcock, Carlos Dominguez and Sucheta Soundararajan).

BOOKS   

  1. An Invitation to Modern Number Theory (with Ramin Takloo-Bighash), Princeton University Press, 2006, 519 pages.
  2. The Mathematics of Encryption: An Elementary Introduction (with Midge Cozzens), AMS Mathematical World series 29, Providence, RI, 2013, 332 pages.
  3. Theory and Applications of Benford's law (senior editor for book, duties include writing chapters and coordinating contributions): Princeton University Press, 2015, 438 pages.
  4. The Probability Lifesaver: Princeton University Press, 2017, 752 pages.
  5. Mathematics of Optimization: How to do things faster: AMS, to appear.
  6. The Pi Mu Epsilon 100th Anniversary Problems (with Stephan Garcia): In preparation.

WILLIAMS STUDENT THESES    Click here for Williams student theses

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RECENT CONFERENCES:  Undergrad Research Panel (Boston 2012)      Undergrad Research Session (HC 2011 and BC 2013)

NOTE: At some point my pages will be migrating to https://sites.williams.edu/sjm1/