Benford's Law, Values of L-functions and the 3x+1 Problem

Details Benford's Law, Values of L-functions and the 3x+1 Problem Benford's Law, Values of L-functions and the 3x+1 Problem

2004-11-30

arxiv.org/abs/math/0412003v2

Acta Arithmetica 120 (2005), no. 3, 269-297

Mathematics

Number Theory

25 pages, 1 figure; replacement of earlier draft (corrected some typos, added more exposition, added results for characteristi

Scientific paper

We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the system. The other is a general technique of applying Poisson Summation to the limiting distribution. We show the distribution of values of L-functions near the central line and (in some sense) the iterates of the 3x+1 Problem are Benford.

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