Chapter 3:
Fourier Analysis and Benford’s Law
(Miller)
Much of this chapter assumes some familiarity with Fourier analysis. The
following is a quick introduction and review, and is taken from "An
Invitation to Modern Number Theory" (by S. J. Miller and R. Takloo-Bighash,
Princeton University Press): Chapter is
available here (there are many references to other parts of the book;
click here for the relevant
bibliography and index).
- Additional Reading:
- V. Cuff, A. Lewis and S. J. Miller, The Weibull distribution
and Benford's law. preprint.
Available online here.
- D. Jang, J. U. Kang, A. Kruckman, J. Kudo and S. J. Miller, Chains of
distributions, hierarchical Bayesian models and Benford's Law}, Journal
of Algebra, Number Theory: Advances and Applications, volume 1, number 1
(March 2009), 37--60. Available
online here.
- J. Lagarias and K. Soundararajan, Benford's Law for the 3x+1 Function,
J. London Math. Soc. 74 (2006), series 2, no. 2, 289--303.
Available online here.
- A. Kontorovich and S. J. Miller, Benford's law, values of L-functions
and the 3x+1 problem, Acta Arith. 120 (2005), 269--297.
Available online here.
- S. J. Miller and M. Nigrini, The Modulo 1 Central Limit Theorem and
Benford's Law for Products, International Journal of Algebra 2
(2008), no. 3, 119--130.
Available online here.
- S. J. Miller and M. Nigrini, Order statistics and Benford's law,
International Journal of Mathematics and Mathematical Sciences, Volume 2008
(2008), Article ID 382948, 19 pages. doi:10.1155/2008/382948.
Available online here.
- Homework Problems:
- Videos:
Return to "Theory and Applications of Benford's Law"
Homepage
Email the editor at sjm1@williams.edu,
Steven.Miller.MC.96@aya.yale.edu