Positional number systems with digits forming an arithmetic progression
type: Item
instance of: scholarly article
title: Positional number systems with digits forming an arithmetic progression
zbMATH Open document ID: 1181.11015
author: Clemens Heuberger
author: Helmut Prodinger
author: Stephan Wagner
published in: Monatshefte für Mathematik
publication date: 2009-06-22T00:00:00Z
review text: In this paper a number system that arises in a natural way in a graph-theoretic context is studied. It is defined by a set of positive digits forming an arithmetic progression and complete residue system modulo the base \(b\) The question how the digits are distributed among the first \(N\) integers is addressed. The authors give an explicit formula for the length of the representation and a explicit formula that gives the \(j\)th digit of the representation of \(n\). A Delange type analysis of the frequencies of digits is based upon such an explicit formula. They also study the averages and obtain asymptotic results involving periodic functions that are completely described via their Fourier coefficients. The Mellin-Perron approach is used.
reviewed by: Takao Komatsu
Mathematics Subject Classification ID: 11A63
zbMATH DE Number: 5567006
zbMATH Keywords: number system
zbMATH Keywords: digit formulae
zbMATH Keywords: digit frequencies
zbMATH Keywords: Mellin-Perron summation formula
MaRDI profile type: Publication
full work available at URL: s00605-008-0008-8
OpenAlex ID: W1986595213
cites work: Sur la fonction sommatoire de la fonction 'somme des chiffres'
cites work: Mellin transforms and asymptotics: Digital sums
cites work: The Sum-of-Digits Function for Complex Bases
cites work: Q4320535
cites work: On minimal expansions in redundant number systems: Algorithms and quantitative analysis
cites work: Maximizing the number of independent subsets over trees with bounded degree
cites work: Q4398780
cites work: Applications of binomial measures to power sums of digital sums
cites work: Q4428920
DOI: 10.1007/S00605-008-0008-8
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description: scientific article; zbMATH DE number 5567006