Distribution of the sum-of-digits function of random integers: a survey

DOI10.1214/12-PS213zbMath1327.60029arXiv1212.6697MaRDI QIDQ462807

Vytas Zacharovas, Louis H. Y. Chen, Hsien-Kuei Hwang

Publication date: 22 October 2014

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6697

zbMATH Keywords

asymptotic normalityStein's methodnumeration systemsKrawtchouk polynomialstotal variation distancesum-of-digits functiondigital sumsGrey codes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Asymptotic results on arithmetic functions (11N37) Combinatorial probability (60C05) Approximations to statistical distributions (nonasymptotic) (62E17) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

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Partial factorizations of products of binomial coefficients ⋮ Computational aspects of sturdy and flimsy numbers ⋮ Asymptotic expansions for linear homogeneous divide-and-conquer recurrences: algebraic and analytic approaches collated ⋮ Identities and periodic oscillations of divide-and-conquer recurrences splitting at half ⋮ From Stein identities to moderate deviations ⋮ Global extrema of the Delange function, bounds for digital sums and concave functions ⋮ Application of extreme sub- and epiarguments, convex and concave envelopes to search for global extrema ⋮ Power and exponential sums for generalized coding systems by a measure theoretic approach ⋮ Unnamed Item ⋮ A Probabilistic Approach to Generalized Zeckendorf Decompositions ⋮ The Estimate of $\chi^2$-Distance between Binomial and Generalized Binomial Distributions ⋮ Dirichlet series associated to sum-of-digits functions

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