Distribution of the sum-of-digits function of random integers: a survey
arXiv:1212.6697 · doi:10.1214/12-PS213
Abstract
We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical probability approach, Stein's method, an analytic approach and a new approach based on Krawtchouk polynomials and the Parseval identity. We also extend the study to a simple, general numeration system for which similar approximation theorems are derived.
60 pages