 RESEARCH INTERESTS:
Analytic Number Theory, Random Matrix Theory,
Probability (zeros and nlevel statistics for
families of Lfunctions, 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 and 2level densities for rational families of elliptic curves:
evidence for the underlying group symmetries.
Compositio Mathematica (140
(2004),
no. 4, 952992).
pdf
 Distribution of eigenvalues for the ensemble
of real symmetric Toeplitz matrices (with Chris Hammond).
Journal of
Theoretical Probability
(18 (2005), no. 3, 537566).
pdf
 Benford's law, values of Lfunctions and the
3x+1 problem (with Alex Kontorovich),
Acta Arithmetica. (120
(2005), no. 3, 269297).
pdf.
 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, 111120, Expanded Version). pdf
 Incomplete exponential
sums in several variables (with Eduardo Duenez,
Howard Straubing, and Amitahba Roy),
Journal of Number Theory
(116 (2006), no. 1, 168199).
pdf
 Closedform Bayesian inferences for the logit model via polynomial expansions (with Eric Bradlow
and Kevin Dayaratna),
Quantitative Marketing and Economics
(4 (2006), no. 2, 173206).
pdf
 Investigations of zeros near the central point of elliptic curve
Lfunctions,
Experimental Mathematics (15 (2006), no. 3,
257279).
pdf
(data available
online).
 The lowlying zeros of a GL(4) and a GL(6) family of
Lfunctions (with
Eduardo Duenez),
Compositio Mathematica
(142 (2006), no. 6,
14031425)
pdf.
 Lowlying zeros of Lfunctions with orthogonal symmetry (with Chris
Hughes),
Duke Mathematical Journal (136
(2007), no. 1, 115172)
pdf
 Constructing oneparameter families of
elliptic curves
over Q(T) with moderate rank (with Scott Arms, Alvaro LozanoRobledo),
Journal of Number Theory. (123
(2007), no 2, 388402
pdf
 A derivation of James' Pythagorean
projection,
By The Numbers  The
Newsletter of the SABR Statistical Analysis Committee (16
(February 2006), no. 1, 1722).
pdf (expanded
version:
pdf).
Chance Magazine (20 (Winter 2007), no. 1, 4048).
 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,
637662.)
pdf
 Benford's Law applied to hydrology data  results and relevance to
other geophysical data (with Mark Nigrini),
Mathematical Geology (39
(2007), no. 5, 469490).
pdf
 When the CramerRao Inequality provides no information,
Communications in Information and Systems.
(7 (2007), no. 3, 265272).
pdf
 The Modulo 1 Central Limit Theorem and Benford's Law for Products
(with Mark Nigrini),
International Journal of Algebra. (2 (2008), no. 3,
119130).
pdf
 A Symplectic Test of the LFunctions Ratios Conjecture,
IMRN (2008). (Vol. 2008, article ID rnm146, 36 pages, doi:10.1093/imrn/rnm146).
pdf
 An identity for sums of polylogarithm functions,
Integers (electronic journal of combinatorial number theory). (8
(2008), A15)
pdf
 A probabilistic proof of Wallis' formula for
π,
American Mathematical Monthly. (115 (2008), no. 8, 740745)
pdf
 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,
231244.)
pdf
 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
 Lower order terms in the 1level density for families of holomorphic
cuspidal newforms,
Acta Arithmetica.
(137 (2009), 5198)
pdf
 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), 3760)
pdf
 An orthogonal test of the Lfunctions Ratios Conjecture,
London Mathematical Society. (2009,
doi:10.1112/plms/pdp009)
pdf
 Silver Scheduler:
DemandDriven 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
 The effect of convolving families of
Lfunctions on the underlying group symmetries (with Eduardo Duenez),
Proceedings of the London Mathematical Society. (2009; doi: 10.1112/plms/pdp018)
pdf
 When almost all sets are difference dominated (with Peter Hegarty),
Random Structures and Algorithms. (35, 2009, no. 1, 118136)
pdf
 Nuclei, primes and the random matrix connection (with Frank W. K.
Firk), invited paper to
Symmetry
(1, (2009), 64105; doi:10.3390/sym1010064)
pdf
 Data diagnostics using second order tests of Benford's Law (with Mark Nigrini),
Auditing: A Journal of Practice and Theory. (28 (2009),
no. 2, 305324. doi: 10.2308/aud.2009.28.2.305)
MSWord file
 Explicit constructions of infinite families of MSTD sets (with
Brooke Orosz and Dan Scheinerman), Journal
of Number Theory (130 (2010) 12211233)
pdf
 A unitary test of the Lfunctions Ratios Conjecture (with John Goes,
Steven Jackson, David Montague, Kesinee Ninsuwan, Ryan Peckner and Thuy
Pham),
Journal of Number Theory.
(130 (2010) 22382258)
pdf
 Towards an `average' version of the Birch and SwinnertonDyer
Conjecture (with John Goes),
Journal of Number Theory (130
(2010), no. 10, 23412358)
pdf
 An Orthogonal Test of the Lfunctions Ratios Conjecture, II (with
David Montague), Acta Arithmetica
(146 (2011), 5390.)
pdf
 Rational irrational proofs (with David Montague),
Mathematics Magazine (85 (2012), no. 2, 110114).
pdf
(expanded version:
pdf;
letter from Nerode and Tennenbaum on history of proof:
pdf)
 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), SpringerVerlag, 2010.
pdf
 Demanddriven scheduling of movies in a multiplex (with Jehoshua
Eliashberg and Charles B. Weinberg),
newsletter of the European Marketing Academy, October 2010
(requested summary of
SilverScheduler paper in honor of it receiving the
International Journal of Market Research Best Paper Award for 2009).
 Effective equidistribution and the SatoTate law for families of
elliptic curves (with M. Ram Murty),
Journal of Number Theory (131
(2011), no. 1, 2544)
pdf
 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
 Isoperimetric Sequences (with Frank Morgan, Edward Newkirk and Lori
Pedersen),
Mathematics Magazine (84 (Feb. 2011), 3742).
pdf
 Distribution of eigenvalues for highly palindromic real symmetric Toeplitz matrices (with Steven Jackson and Thuy Pham), Journal of
Theoretical Probability. (25
(2012), 464495)
pdf
 A combinatorial identity for studying SatoTate type problems (with
M. Ram Murty and F. Strauch),
Rendiconti del Seminario Matematico (68 (2010), no. 4,
337348).
pdf
 Moments of the rank of elliptic curves (with Siman Wong), Canadian Journal of Mathematics
(64 (2012), no. 1, 151182)
pdf
 The `Real' Schwarz lemma (with David Thompson):
American Mathematical Monthly. (118 (October 2011),
no. 8, page 725)
pdf
 An elliptic curve family test of the Ratios Conjecture (with Duc
Khiem Huynh and Ralph Morrison),
Journal of Number Theory
(131 (2011), 11171147)
pdf
 On the number of summands in Zeckendorf decompositions (with Gene S. Kopp, Murat Koloğlu and Yinghui
Wang),
Fibonacci Quarterly. (49 (2011), no 2, 116130)
pdf
 Generalized More Sums Than Differences Sets (with Geoffrey Iyer, Oleg Lazarev and Liyang
Zhang), Journal of Number Theory.
(132 (2012), no. 5, 10541073)
pdf
 Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets (with Luc Robinson and Sean Pegado).
INTEGERS
(12, #A30 2012).
pdf
 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
 From Fibonacci Numbers to Central Limit Type Theorems (with Yinghui
Wang),
Journal of Combinatorial Theory, Series A. (7 (2012),
13981413)
pdf (expanded arxiv version)
 First Order Approximations of the Pythagorean WonLoss 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, 1519).
 Lowlying zeros of number field Lfunctions (with Ryan Peckner),
Journal of Number Theory.
(132 (2012), 28662891) pdf
 Quadratic fields with cyclic 2class groups (with Carlos Dominguez
and Siman Wong):
Journal of Number Theory
(133 (2013), no. 3, 926939).
pdf
 Leading, learning and herding (with Daniel Stone),
Mathematical Social Sciences (65 (2013), 222231) pdf
 The Pythagorean WonLoss 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
193209)
pdf
 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), 1327).
pdf
 Closed Form Continued Fraction Expansions of Special Quadratic
Irrationals (with Dan Fishman),
ISRN Combinatorics. (vol. 2013, Article ID 414623, 5 pages)
pdf
(journal
version)
 Distribution of Missing Sums in Sumsets (with Oleg Lazarev and Kevin
O'Bryant),
Experimental Mathematics (22 (2013), no. 2, 132156).
pdf
 The nlevel densities of lowlying zeros of quadratic Dirichlet
Lfunction (with Jake Levinson),
Acta Arithmetica.
(161 (2013), 145182)
pdf
(Mathematica files available here)
 Viruslike dynamics on starlike graphsviruslike dynamics on starlike
graphs (with Thealexa
Becker, Alec GreavesTunnell, Leo Kontorovich, Amitabha Roy, Karen Shen),
the Journal of Nonlinear
Systems and Applications (4 2013), no. 15363).
pdf
 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,
10201060) pdf
 Coordinate sum and difference sets of ddimensional modular
hyperbolas (with Amanda Bower, Ron Evans and Victor Luo),
INTEGERS (#A31, 2013, 16 pages)
pdf (expanded arxiv version:
pdf)
 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, 513534).
pdf
 The lowlying zeros of level 1 Maass forms (with Levent Alpoge),
IMRN. (2014,
24 pages,
doi:10.1093/imrn/rnu012)
pdf
 Special Sets of Primes in Function Fields (with Julio Andrade, Kyle
Pratt and MinhTam Trinh),
INTEGERS. (14 (2014), #A18)
pdf
 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), 136158)
pdf
 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, SpringerVerlag, 2014,
pages 89114).
pdf
 A Generalization of Fibonacci FarDifference Representations and
Gaussian Behavior (with Philippe Demontigny, Thao Do, Archit
Kulkarni and Umang Varma),
Fibonacci Quarterly (52 (2014), no. 3, 247273)
pdf
 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, 577608).
pdf
 Newman's conjecture in various settings (with Julio Andrade and Alan
Chang), Journal of Number Theory.
(144 (2014), 7091)
pdf
 Maass waveforms and lowlying 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), SpringerVerlag
2015.
pdf
 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 113).
pdf
 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 7998).
pdf
 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 147157)
pdf
 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 159173).
pdf
 The Pi Mu Epsilon 100th Anniversary Problems: Part III (with many of
my students),
The Pi Mu
Epsilon Journal (14 (2014), no. 1, 6599).
pdf
 Continued Fraction Digit Averages and Maclaurin's Inequalities (with
Francesco Cellarosi, Doug Hensley and Jake Wellens),
Experimental Mathematics (24 (2015), no. 1, 2344)
pdf
 The \(n\)Level Density of Dirichlet \(L\)Functions over \(\mathbb{F}_q[T]\)
(with Julio Andrade, Kyle Pratt and MinhTam Trinh),
Communications in Number Theory and Physics. (8 (2014), no.
3, 511539)
pdf
 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
 The Pi Mu Epsilon 100th Anniversary Problems: Part IV (with many of
my students),
The Pi Mu Epsilon Journal (15 (2015), no. 2, 100134)
pdf
 The James Function (with Christopher N. B. Hammond and Warren P.
Johnson),
Mathematics Magazine. (88 (2015), 5471).
pdf

Benford Behavior of Zeckendorf
Decompositions (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, C.
TurnageButterbaugh and M. Weinstein),
Fibonacci Quarterly. (52
(2014), no. 5, 3546)
pdf
 Gaussian Behavior of the Number of
Summands in Zeckendorf Decompositions in Small Intervals (with A. Best,
P. Dynes, X. Edelsbrunner, B. McDonald C. TurnageButterbaugh and M.
Weinstein),
Fibonacci Quarterly. (52
(2014), no. 5, 4753)
pdf
 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
 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
 Relieving and Readjusting Pythagoras (with Victor Luo),
By The Numbers  The
Newsletter of the SABR Statistical Analysis Committee. (25
(2015), no. 1, 514)
pdf
(older, expanded version:
pdf)
 Sums and Differences of Correlated Random Sets (with Thao Do, Archit
Kulkarni, David Moon and Jake Wellens) Journal of Number Theory. (147
(2015), 4468)
pdf
 Generalizing Zeckendorf's Theorem: The
Kentucky Sequence (with M. Catral, P. Ford, P. Harris and D. Nelson),
Fibonacci Quarterly. (52
(2014), no. 5, 6890)
pdf
 Gaps between zeros of GL(2) Lfunctions
(with Owen Barrett, Brian McDonald, Ryan Patrick, Caroline
TurnageButterbaugh and Karl Winsor),
Journal of Mathematical Analysis and Applications. (429
(2015), 204232)
pdf
 Surpassing the Ratios Conjecture in the 1level density of Dirichlet
Lfunctions (with Daniel Fiorilli),
Algebra & Number Theory (9
(2015), no. 1, 1352)
pdf
(expanded arXiv version)
 Gaps between summands in generalized Zeckendorf decompositions
(with Amanda Bower, Rachel Insoft, Shiyu Li and Philip Tosteson, and an
appendix with Iddo BenAri),
Journal of Combinatorial Theory, Series A. (135 (2015),
130160)
pdf
 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), 123153)
pdf
 Newman's Conjecture in Function Fields
(with Alan Chang, David Mehrle, Tomer Reiter, Joseph Stahl and Dylan
Yott),
Journal of Number Theory. (15
(2015), 154169)
pdf
 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
 LowerOrder Biases in Elliptic Curve
Fourier Coefficients in Families (with Blake Mackall, Christina Rapti
and Karl Winsor), Frobenius Distributions: LangTrotter and SatoTate
Conjectures (David Kohel and Igor Shparlinski, editors), Contemporary
Mathematics 663, AMS, Providence, RI 2016. pdf
 From Quantum Systems to LFunctions: Pair Correlation Statistics and
Beyond (with Owen Barrett, Frank W. K. Firk and Caroline
TurnageButterbaugh), Open Problems in Mathematics (editors
John Nash Jr. and Michael Th. Rassias, SpringerVerlag, 2016).
pdf
 Determining Optimal Test Functions for Bounding the Average Rank in
Families of LFunctions} (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
 The Weibull distribution and Benford's Law (with Victoria Cuff and
Allie Lewis),
Involve (85 (2015), 859874. DOI 10.2140/involve.2015.8.859).
pdf
 Some Results in the Theory of Lowlying Zeros (with Blake Mackall,
Christina Rapti, Caroline TurnageButterbaugh 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, SpringerVerlag.
pdf
 Leading Digit Laws on Linear Lie Groups (with Corey Manack),
Research in Number Theory (1:22 (2015), DOI
10.1007/s4099301500244).
pdf
 Gaussian Distribution of the Number of
Summands in Generalized Zeckendorf Decompositions in Small Intervals
(with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald C. TurnageButterbaugh
and M. Weinstein),
INTEGERS (16 (2016), #A6)
pdf
 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
 Multiple Regression Analysis: Understanding the Impact of Offensive
and Defensive Contributions to Team Performance (with Kevin D. Dayaratna),
The Hockey Research Journal (2014/2015, 4143).
pdf
 A Probabilistic Approach to Generalized Zeckendorf Decompositions
(with Iddo BenAri),
SIAM Journal on Discrete Mathematics (30 (2016), no. 2,
13021332)
pdf
(journal version here)
 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, 2736).
pdf
 A Generalization of Zeckendorf's Theorem via Circumscribed mgons
(with Robert Dorward, Pari L. Ford, Eva Fourakis, Pamela E. Harris,
Eyvindur A. Palsson and Hannah Paugh), to appear in
Involve.
pdf
 GeometricProgressionFree 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, 242262). pdf
 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, 197207)
pdf (pruned
published version:
pdf:
Copyright [2017] Mathematical Association of America. All Rights
Reserved.).
 Legal Decompositions Arising from Nonpositive Linear Recurrences
(with Minerva Catral, Pari Ford, Pamela Harris, Steven J. Miller, Dawn
Nelson),
Fibonacci Quarterly (54 (2016), no. 4, 348365).
pdf
(journal version:
pdf)
 Subsets of \(\mathbb{F}_q[x]\) Free of 3term Geometric Progressions
(with Megumi Asada, Eva Fourakis, Sarah Manski, Gwyneth Moreland and
Nathan McNew),
Finite Fields and their Applications (44 (2017), 135147)
pdf
 Fringe pairs in generalized MSTD sets (with Megumi Asada, Sarah Manski and Hong
Suh),
International
Journal of Number Theory. (13 (2017), no. 2,
26532675)
pdf
 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, 5265).
pdf
 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, 105114).
pdf
 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, 135143).
pdf
 If a prime divides a product (with Cesar Silva),
College Mathematics Journal. (48 (2017), no. 2, 123128)
pdf
 New Behavior in Legal Decompositions Arising from Nonpositive
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, 252275). pdf
 The Emergence of 4Cycles in Polynomial
Maps over the Extended Integers (with Andrew Best, Patrick Dynes,
Jasmine Powell and Ben Weiss,
Minnesota Journal of
Undergraduate Mathematics. (2 (20162017), no. 1, 15
pages) pdf
 Lowlying zeros for Lfunctions associated to Hilbert modular forms
of large level) (with ShengChi Liu),
Acta Arithmetica
(180 (2017), 251266)
pdf
 Constructing families of moderaterank elliptic curves over number
fields (with David Mehrle, Tomer Reiter, Joseph Stahl and Dylan
Yott),
Minnesota Journal of
Undergraduate Mathematics (2 (20162017), 11 pages)
pdf
 Benford Behavior of Generalized
Zeckendorf Decompositions (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald C. TurnageButterbaugh
and M. Weinstein), Combinatorial and Additive Number Theory II: CANT,
New York, NY, USA, 2015 and 2016, Springer, New York, 2017.
pdf
 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
 OneLevel 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/s4099301700919) pdf
 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),
143154)
pdf
 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, 421429)
pdf
 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
 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), 407427).
pdf
 Optimal point sets determining few distinct triangles (with Alyssa
Epstein, Adam Lott and Eyvindur Palsson),
INTEGERS. (18 (2018), Paper No. A16, 17 pp.).
pdf
 Benford's Law and Continuous Dependent Random Variables (with Thealexa Becker,
David Burt, Taylor C. Corcoran, Alec GreavesTunnell, Joseph R.
Iafrate, Joy Jing, Jaclyn D. Porfilio, Ryan Ronan, Jirapat Samranvedhya,
Blaine Talbut
and Frederick W. Strauch), (388 (2018), 350381)
Annals of Physics.
pdf.
 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
 Spectral Statistics of NonHermitian 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
 The bidirectional ballot polytope (with Carsten Peterson, Carsten
Sprunger and Roger Van Peski),
INTEGERS (81 (2018), #A81, 118)
pdf
 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/s4099301801377)
pdf
 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)
 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
 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, 109125)
pdf
 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, 201212) pdf
 Central Limit Theorems for Gaps of Generalized Zeckendorf
Decompositions (with Ray Li),
Fibonacci Quarterly. (57 (2019), no. 3, 213230) pdf
 The Zeckendorf Game (with Paul BairdSmith, Alyssa Epstein and
Kristen Flint), to appear in the Proceedings of CANT 2018.
pdf
 A geometric perspective on the MSTD question (with Carsten
Peterson),
Discrete and Computational Geometry. (62 (2019), no. 4,
832855):
https://doi.org/10.1007/s00454019001097)
pdf
 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
 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
 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), 143156),
pdf
 Infinite Families of Partitions into MSTD Subsets (with Hung Chu,
Noah Luntzlara and Lily Shao),
INTEGERS. (19 (2019), #A60)
pdf
 On Near Perfect Numbers (with Peter Cohen, Katherine Cordwell,
Alyssa Epstein, Chung Hang Kwan and Adam Lott)
Acta Arithmetica.
(194 (2020), no. 4, 341366)
pdf
 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)
pdf
 The Generalized Zeckendorf Game (with Paul BairdSmith, Alyssa
Epstein and Kristen Flint),
Fibonacci Quarterly (57 (2019) no. 5, 114)
pdf
 Benford's Law Beyond Independence: Tracking Benford Behavior in
Copula Models (with Becky Durst).
Involve (19 (2020), no. 7, 11931218)
pdf
 The Fibonacci Quilt Game (with Alexandra Newlon),
Fibonacci Quarterly (2 (2020), 157168)
pdf
 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
 Extensions of Autocorrelation Inequalities with Applications to
Additive Combinatorics (with Sara Fish and Dylan King),
Bulletin of the Australian Mathematical Society (2020, 111,
doi:10.1017/S000497272000026X).
pdf
 Central Limit Theorems for Compound Paths on the 2Dimensional
Lattice (with Evan Fang, Jonathan Jenkins, Zack Lee, Daniel Li, Ethan
Lu, Dilhan Salgado, Joshua Siktar),
Fibonacci Quarterly. (3 (2020), 208225)
pdf

Higher Order Fibonacci Sequences from Generalized Schreier
sets (with Hung Viet Chu, Zimu Xiang),
Fibonacci Quarterly. (3 (2020), 249253)
pdf
 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), 95109).
pdf
 On the sum of kth powers in terms of earlier sums (with Enrique
Trevino), to appear in the
College Mathematics Journal. (48 (2020), no. 2, 123128)
(arxiv version:
pdf)
 Recurrence Relations and Benford's Law (with Madeleine Farris, Noal
Luntzlara, Lily Shao and Mengxi Lang),
Statistical Methods and Applications. (2020: DOI:
https://doi.org/10.1007/s10260020005471)
pdf
 Extending Zeckendorf's Theorem to a Nonconstant Recurrence and the
Zeckendorf Game on this Nonconstant 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), 5576)
pdf
 Deterministic Zeckendorf Games (with Ruoci Li, Xiaonan Li, Clay
Mizgerd, Chenyang Sun, Dong Xia, And Zhyi Zhou),
Fibonacci Quarterly. (58 (2020), no. 5, 152160)
pdf
 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), to appear in the
Fibonacci Quarterly.
pdf
 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)
 Generalizing Zeckendorf's Theorem to a Nonconstant Recurrence (with
E. Boldyriew, A. Cusenza, L. Dai, P. Ding, A. Dunkelberg, J. Haviland,
K. Huffman, D. Ke, D. Kleber, J. Kuretski, J. Lentfer, T. Luo, C. Mizgerd, V. Tiwari, J. Ye, Y. Zhang, X. Zheng and Weiduo Zhu),
to appear in the
Fibonacci Quarterly.
pdf
 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, 7790)
pdf
 Lessons from the German Tank Problem (with George Clark and Alex
Gonye), to appear in the
Mathematical Intelligencer.
pdf
 Zeckendorf's Theorem Using Indices in an Arithmetic
Progression} (with Amelia Gilson, Hadley Killen, Tamas Lengyel, Nadia
Razek, Joshua M. Siktar, and Liza Sulkin, to appear in the
Fibonacci Quarterly.
pdf
 When Rooks Miss: Probability through Chess (with Daniel Turek, Haoyu
Sheng), to appear in the
College Mathematics Journal.
pdf
 Generalizing RuthAaron Numbers (with Nancy Jiang), The PUMP Journal
of Undergraduate Research (4 (2021), 2062)
pdf
 LowerOrder Biases Second Moments of Dirichlet Coefficients in
Families of LFunctions (with Megumi Asada, Ryan Chen, Eva Fourakis,
Yujin Kim, Andrew Kwon, Jared Lichtman, Blake Mackall, Eric Winsor, Karl
Winsor, Jianing Yang, Kevin Yang; appendices with Roger Weng and
Michelle Wu), to appear in
Experimental Mathematics,
pdf
 On Zeckendorf related partitions using the Lucas sequence (with Hung
Viet Chu and David Luo), submitted to the
Fibonacci Quarterly.
pdf
(arxiv version:
pdf)

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, 375478).
pdf
 Constructions of Generalized MSTD Sets in Higher Dimensions (with
Elena Kim). to appear in the
Journal of Number Theory
pdf
 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
 Classification of crescent configurations (with Rebecca F. Durst,
Max Hlavacek, Chi Huynh, Steven J. Miller and Eyvindur A. Palsson),
submitted to
INTEGERS.
pdf
 Avoiding 3Term Geometric Progressions in NonCommutative Settings
(with Megumi Asada, Eva Fourakis, Eli Goldstein, Sarah Manski, Nathan
McNew and Gwyneth Moreland), submitted to the Journal of Integer
Sequences.
pdf
 The Explicit SatoTate Conjecture For Primes In Arithmetic
Progressions (with Trajan Hammonds, Casimir Kothari, Noah Luntzlara,
Jesse Thorner, Hunter Wieman), submitted May 2019 to
IJNT.
pdf
 Rank and Bias in Families of Hyperelliptic Curves via Nagao's
Conjecture} (with Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon,
Alvaro LozanoRobledo). Submitted October 2019 to the Journal of Number Theory
pdf (arxiv) or
pdf
 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
 Distribution of missing differences in diffsets (with Scott
HarveyArnold and Fei Peng),
pdf
 Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences,
I
(with Thomas Martinez, Clay Mizgerd and Chenyang Sun), submitted to the
Fibonacci Quarterly.
pdf
 Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences,
II
(with Thomas Martinez, Clay Mizgerd, Jack Murphy and Chenyang Sun), submitted to the
Fibonacci Quarterly.
pdf
 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). submitted to
Experimental Mathematics
pdf
 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), submitted to the
Fibonacci Quarterly.
pdf
 The limiting spectral measure for an ensemble of generalized
checkerboard matrices (with Fangu Chen, Yuxin Lin and Jiahui Yu).
pdf
 An Introduction to Completeness of Positive Linear Recurrence
Sequences (with Ela
Boldyriew, John Haviland, Phuc Lam, John Lentfer, Fernando Trejos
Suarez).
pdf
 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
 Walking to Infinity Along Some Number Theory sequences (with Fei
Peng, Tudor Popescu, Joshua M. Siktar, Nawapan Wattanawanichkul, and the
Polymath REU Program),
pdf
 Walking to Infinity on primes in $\mathbb{Z}[\sqrt{2}]$ (with
Bencheng Li, Tudor Popescu, Daniel Sarnecki and Nawapan Wattanawanichkul),
submitted to the Journal of Integer Sequences.
pdf
 Determining optimal test functions for 2level densities} (with
Elzbieta Boldyriew, Fangu Chen, Charles Devlin VI, Jason Zhao).
pdf
 Biases in Moments of the Dirichlet Coefficients in One and
TwoParameter Families of Elliptic Curves (with Y. Yeng and an appendix
by J. Wu),
submitted to The PUMP Journal
of Undergraduate Research.
pdf
PREPRINTS / IN PREPARATION (available upon
request)
 The Ratios Conjecture and Convolving Families of \(L\)functions
(with MinhTam Trinh).
 When Generalized Sumsets are Difference Dominated (with Virginia
Hogan).
pdf
 Moment Formulas for Ensembles of Classical Compact Groups (with Geoffrey Iyer
and Nicholas Triantafillou)
 \(m\)Paths and the \(3x+1\) Problem (with Bruce Adcock, Carlos Dominguez
and Sucheta
Soundararajan).
 On WithinPerfectness and NearPerfectness (with Peter Cohen,
Katherine Cordwell, Alyssa Epstein, Chung Hang Kwan and Adam Lott)
pdf
BOOKS

An Invitation to Modern Number Theory (with Ramin TaklooBighash),
Princeton University Press, 2006, 519 pages.

The Mathematics of Encryption: An Elementary Introduction (with Midge
Cozzens), AMS Mathematical World series 29, Providence, RI, 2013, 332 pages.

Theory and Applications of Benford's
law (senior editor for book, duties include writing chapters and
coordinating contributions): Princeton University Press, 2015, 438
pages.

The Probability Lifesaver: Princeton University Press, 2017, 752
pages.
 Mathematics of Optimization: How to do things faster: AMS, to
appear.
 The Pi Mu Epsilon 100th Anniversary Problems (with Stephan Garcia):
In preparation.
WILLIAMS STUDENT THESES
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 Williams Classes: 20162017: FALL:
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 Analysis:
Math 209 (Differential Equations
and Vector Calculus),
Math 372
(Complex Analysis),
Math 389 (Advanced
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 Applied Analysis:
Math 317
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Math 416 (Advanced
Applied Linear Programming)
 Probability and Stats:
Math 317
(Operations Research),
Math/Stat 341
(Probability '15)
 Problem Solving:
Math 331 (The little Questions),
 Number Theory:
Math 10
(cryptography, winter study),
Math 308/406
(Analysis and Number Theory), Math 389
(Advanced Analysis),
Math 406
(Analysis and Number Theory);
 Senior Seminars:
Math 308/406
(Analysis and Number Theory), Math 406
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Math 416 (Advanced
Applied Linear Programming)
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2010), Math
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 Smith / Mount Holyoke:
Math 238 (number
theory, Smith 2011),
Math/Stat 342
(Probability, MH 2011),
Math
395 (Linear Programming, MH 2011)
 Brown:
Math
1 (freshman seminar: riddles to modern mathematics), Math 90 (calc
I,
summer calc I),
Math 35
(honors multivariable calculus),
Math
52 (linear algebra),
Math 54
(honors linear algebra),
Math 153 (abstract
algebra),
Math 162
(mathematical statistics), Math 197 (Benford's
law,
sabermetrics)
 Ohio State:
Math 104 (Basic College
Math),
Math 148 (Algebra/Trig),
Math 187/487 (Problem / Advanced
Problem Solving),
Math 683L (Grad
Linear Algebra), Working groups (Euler,
fractals)
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2011,
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2013,
2014 Math Moments:
2015
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BC 2013)