Multiplicative functions with regularity properties. I
type: Item
instance of: scholarly article
title: Multiplicative functions with regularity properties. I
zbMATH Open document ID: 0532.10003
DOI: 10.1007/BF01956777
published in: Acta Mathematica Hungarica
publication date: 1983-01-01T00:00:00Z
review text: The author studies multiplicative functions which satisfy some kind of asymptotic recursion relation. A typical result (Theorem 2.1) is the following. Let \(B\in\mathbb{N}\) be fixed. On the set of positive integers which are coprime to \(B\) assume (a) \(f\) multiplicative, (b) \(| f(n)| =1, c\), \(f(n+B)-f(n)=O(n^{-\gamma})\) \((n\to \infty,\ \gamma>0)\) Then \(f(n)=\chi_B(n) n^{i\tau}\) for \((n,B)=1\), where \(\chi_B\) is a character mod \(B\). The proofs are elementary. For Part II see the following review Zbl 0532.10004.
reviewed by: Dieter Wolke
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 3843824
zbMATH Keywords: regularity properties
zbMATH Keywords: multiplicative functions
zbMATH Keywords: asymptotic recursion relation
author: Imre Kátai
MaRDI profile type: Publication
cites work: Q3937468
cites work: On the regularity of arithmetic multiplicative functions. I, II
cites work: Q3661675
full work available at URL: https://doi.org/10.1007/bf01956777
OpenAlex ID: W4245415987
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description: scientific article; zbMATH DE number 3843824