Benford's law, values of L-functions and the 3x+1 problem

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.

Locations

• Acta Arithmetica - View - PDF
• arXiv (Cornell University) - View - PDF
• DataCite API - View