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WEAK PROPER DISTRIBUTION OF VALUES OF MULTIPLICATIVE FUNCTIONS IN RESIDUE CLASSES

Part of: Multiplicative number theory

Published online by Cambridge University Press:  04 February 2013

WŁADYSŁAW NARKIEWICZ
WŁADYSŁAW NARKIEWICZ*
Affiliation:
Institute of Mathematics, Wrocław University, Plac Grunwaldzki 2-4, PL-50-384 Wrocław, Poland email narkiew@math.uni.wroc.pl
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Abstract

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For a class of multiplicative integer-valued functions $f$ the distribution of the sequence $f(n)$ in restricted residue classes modulo $N$ is studied. We consider a property weaker than weak uniform distribution and study it for polynomial-like multiplicative functions, in particular for $\varphi (n)$ and $\sigma (n)$.

Keywords

multiplicative functionsEuler functionsum of divisorsRamanujan τ-function

MSC classification

Secondary: 11N37: Asymptotic results on arithmetic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 1-2 , October 2012 , pp. 173 - 188
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

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