Benford's law, values of L-functions and the 3x+1 problem
By Alex Kontorovich, Steven J. Miller. 2004
57 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Information Systems, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ce7d24fb1263338917ef5dabeacb1f4b67710919
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Citations in the corpus
- The 3x+1 Problem: An Annotated Bibliography, II (2000-2009) (2006, unknown): “(MR 2007h:37007) Kontorovich and Miller (2005) proved results concerning Benford’s law for initial 3x + 1 iterates, in a double limit as the number of iterates N → ∞.”
- Almost all orbits of the Collatz map attain almost bounded values (2019, background): “17) is the main reason why we work with logarithmic density instead of natural density in this paper (see also [11], [15] for a closely related “Benford’s law” phenomenon).”