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Multiplicative functions on arithmetic progressions

Published online by Cambridge University Press:  26 February 2010

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
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
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3.Halasz, G.. On the distribution of additive and the mean values of multiplicative arithmetic functions. Studia Scient. Math. Hungarica, 6 (1971), 211233.Google Scholar
4.Wirsing, E.. Das asymptotische Verhalten von Summen über multiplikative Funktionen, II. Acta Math. Acad. Sci. Hung., 18 (1967), 411467.Google Scholar