The distribution of generalized sum-of-digits functions in residue classes
type: Item
instance of: scholarly article
title: The distribution of generalized sum-of-digits functions in residue classes
zbMATH Open document ID: 0999.11043
author: Abigail Hoit
published in: Journal of Number Theory
publication date: 2002-10-20T00:00:00Z
review text: A function \(f:\mathbb{N}\to\mathbb{Z}\) has limit distribution modulo \(m\) if the limit \[ \lim_{N\to\infty} \tfrac{1}{N} \#\{0\leq n< N: f(n)\equiv k\bmod m\} \] exists for each integer \(k\); it is called uniform if this limit is always \(\frac{1}{m}\). The author proves a necessary and sufficient criterion for uniform distribution modulo \(m\) in the case, that \(m\) is prime and the function \(f\) is \(Q\)-additive with respect to a base-\(Q\) representation in a general numeration system. This generalizes a known result of the sum-of-digit function.
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11N69
Mathematics Subject Classification ID: 11A63
zbMATH DE Number: 1420251
zbMATH Keywords: distribution of arithmetical functions
zbMATH Keywords: uniform distribution modulo \(m\)
zbMATH Keywords: \(Q\)-additive function
zbMATH Keywords: general numeration system
reviewed by: Jürgen Spilker
MaRDI profile type: Publication
full work available at URL: jnth.1999.2424
OpenAlex ID: W1994977608
cites work: Q4163601
cites work: Sur les fonctions q-additives ou q-multiplicatives
cites work: Systems of Numeration
cites work: Sur les nombres qui ont des propriétés additives et multiplicatives données
cites work: Q3996192
cites work: Q5599324
cites work: Q4234477
DOI: 10.1006/JNTH.1999.2424
description: scientific article; zbMATH DE number 1420251