Weak uniform distribution of \(u_{n+1}=au_ n+b\) in Dedekind domains
type: Item
instance of: scholarly article
title: Weak uniform distribution of \(u_{n+1}=au_ n+b\) in Dedekind domains
zbMATH Open document ID: 0652.10008
DOI: 10.1007/BF01153578
author: Gerhard Turnwald
author: Robert F. Tichy
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155298
review text: Let \(R\) be a Dedekind domain and \(I\) a non-trivial ideal of it. The authors consider sequences \((u_ n)\) in \(R\), satisfying the recurrence \(u_{n+1}=au_ n+b\) and give necessary and sufficient conditions (in terms of \(a, b, u_ 0)\) for such a sequence to be weakly uniformly distributed (mod \(I\)). As a corollary they obtain that such a sequence is weakly uniformly distributed (mod \(I\)) if and only if the congruence \(u_ x\equiv a\pmod I\) is solvable for every \(a\) prime to \(I\).
reviewed by: Władysław Narkiewicz
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 11K06
zbMATH DE Number: 4063180
zbMATH Keywords: weak uniform distribution
zbMATH Keywords: Dedekind domain
zbMATH Keywords: recurrence
MaRDI profile type: Publication
cites work: Weakly uniform distribution mod m for certain recursive sequences and for monomial sequences
cites work: Q3815364
cites work: Uniform distribution of sequences of integers in residue classes
cites work: Q4149833
cites work: Equidistribution of linear recurring sequences in finite fields, II
cites work: Q5659654
cites work: Uniform distribution of recurrences in Dedekind domains
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description: scientific article; zbMATH DE number 4063180