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Kontorovich, AV and Miller, SJ (2005)

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

Acta Arithmetica 120(3), pp. 269-297.

ISSN/ISBN: 0065-1036 DOI: 10.4064/aa120-3-4

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.

@article {MR2188844, AUTHOR = {Kontorovich, Alex V. and Miller, Steven J.}, TITLE = {Benford's law, values of {$L$}-functions and the {$3x+1$} problem}, JOURNAL = {Acta Arith.}, FJOURNAL = {Acta Arithmetica}, VOLUME = {120}, YEAR = {2005}, NUMBER = {3}, PAGES = {269--297}, ISSN = {0065-1036}, CODEN = {AARIA9}, MRCLASS = {11K06 (11B37 11M06 37A45)}, MRNUMBER = {2188844 (2007c:11085)}, MRREVIEWER = {J. C. Lagarias}, DOI = {10.4064/aa120-3-4}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Number Theory