- Probab. Surveys
- Volume 11 (2014), 177-236.
Distribution of the sum-of-digits function of random integers: A survey
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.
Probab. Surveys, Volume 11 (2014), 177-236.
First available in Project Euclid: 10 October 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems 60C05: Combinatorial probability
Secondary: 62E17: Approximations to distributions (nonasymptotic) 11N37: Asymptotic results on arithmetic functions 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
Chen, Louis H. Y.; Hwang, Hsien-Kuei; Zacharovas, Vytas. Distribution of the sum-of-digits function of random integers: A survey. Probab. Surveys 11 (2014), 177--236. doi:10.1214/12-PS213. https://projecteuclid.org/euclid.ps/1412947841