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Multiplicative functions on arithmetic progressions

Published online by Cambridge University Press:  26 February 2010

P. D. T. A. Elliott
P. D. T. A. Elliott
Affiliation:
Department of Mathematics, University of Colorado, Boulder, Colorado 80309, U.S.A.
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Extract

In this paper I show that complex-valued multiplicative functions g which satisfy |g(n)|≤1 for all positive integers n, are generally well distributed in residue classes to small moduli.

Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 199 - 206
Copyright
Copyright © University College London 1987

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References

1.Elliott, P. D. T. A.. Probabilistic Number Theory I: Mean-Value Theorems, II: Central Limit Theorems. Grund. der math. Wiss. 239, 240, (Springer, New York, 1979, 1980).Google Scholar
2.Halász, G.. On the distribution of additive arithmetic functions. Acta Arilhmetica, 27 (1975), 143–152.CrossRefGoogle Scholar
3.Halasz, G.. On the distribution of additive and the mean values of multiplicative arithmetic functions. Studia Scient. Math. Hungarica, 6 (1971), 211–233.Google Scholar
4.Wirsing, E.. Das asymptotische Verhalten von Summen über multiplikative Funktionen, II. Acta Math. Acad. Sci. Hung., 18 (1967), 411–467.Google Scholar