Distribution of the sum-of-digits function of random integers: a survey
Probability
2014-10-14 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.1212.6697,
title = {Distribution of the sum-of-digits function of random integers: a survey},
author = {Louis H. Y. Chen and Hsien-Kuei Hwang and Vytas Zacharovas},
journal= {arXiv preprint arXiv:1212.6697},
year = {2014}
}
Comments
60 pages