On the mean values of multiplicative functions on arithmetic progressions
type: Item
instance of: scholarly article
title: On the mean values of multiplicative functions on arithmetic progressions
zbMATH Open document ID: 0637.10038
DOI: 10.1007/BF01240460
author: S. T. Tulyaganov
published in: Mathematical Notes
publication date: 1987-01-01T00:00:00Z
review text: Asymptotic formulas are given with remainder terms for the summation of complex-valued multiplicative functions on residue classes. The sum \(\sum_{n\leq x, n\equiv k (mod m)}f(n)\) is considered under the assumption that \[ \sum_{p\leq x, p\equiv j (mod m)}g(p)\log p=\alpha x+O(x\eta (x)) \] holds for all j coprime to m, and the remainder is estimated in terms of the function \(\eta\) (x); the results are too complicated to quote in detail.
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 4037941
zbMATH Keywords: mean value theorems
zbMATH Keywords: sums of exponentially multiplicative functions
zbMATH Keywords: Asymptotic formulas
zbMATH Keywords: remainder terms
zbMATH Keywords: multiplicative functions on residue classes
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
cites work: Q3867877
cites work: Q3342663
cites work: Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen
cites work: Asymptotic of mean values of multiplicative functions
description: scientific article; zbMATH DE number 4037941