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2014 Distribution of the sum-of-digits function of random integers: A survey
Louis H. Y. Chen, Hsien-Kuei Hwang, Vytas Zacharovas
Probab. Surveys 11(none): 177-236 (2014). 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.

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Louis H. Y. Chen. Hsien-Kuei Hwang. Vytas Zacharovas. "Distribution of the sum-of-digits function of random integers: A survey." Probab. Surveys 11 177 - 236, 2014. https://doi.org/10.1214/12-PS213

Information

Published: 2014
First available in Project Euclid: 10 October 2014

zbMATH: 1327.60029
MathSciNet: MR3269227
Digital Object Identifier: 10.1214/12-PS213

Subjects:
Primary: 60C05, 60F05
Secondary: 11K16, 11N37, 62E17

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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