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.
Bibtex:
@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 = {http://dx.doi.org/10.4064/aa120-3-4},
}
Reference Type: Journal Article
Subject Area(s): Number Theory