  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.
