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

Alex V. Kontorovich·Steven J. Miller
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Abstract

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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Alex V. Kontorovich, Steven J. Miller. 2005-06-27. Benford's Law, Values of L-functions and the 3x+1 Problem. https://doi.org/10.4064/aa120-3-4

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