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\nconditions follow Benford's Law. For each system proving this involves two main\ningredients. One is a structure theorem of the limiting distribution, specific\nto the system. The other is a general technique of applying Poisson Summation\nto the limiting distribution. We show the distribution of values of L-functions\nnear the central line and (in some sense) the iterates of the 3x+1 Problem are\nBenford.\n