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On a Result of Smith and Subbarao Concerning a Divisor Problem

Published online by Cambridge University Press:  20 November 2018

Werner Georg Nowak
Werner Georg Nowak*
Affiliation:
Institut für Mathematik, Universität für Bodenkultur, Gregor Mendel-Strasse 33 A-1180 Vienna, Austria
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Abstract

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Let d(n;l,k) denote the number of divisors of the positive integer n which are congruent to I modulo k. The objective of the present paper is to prove that (for some exponent θ<⅓)

holds uniformly in l, k and x satisfying 1≤l≤k≤x. This improves a recent result due to R. A. Smith and M. V. Subbarao [3].

Keywords

10H2510L20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 501 - 504
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Van der Corput, J. G., Neue zahlentheoretische Abschätzungen, Math. Ann. 89 (1923), 215-254.10.1007/BF01455979CrossRefGoogle Scholar
2. Hlawka, E., Theorie der Gleichverteilung, Mannheim-Wien-Zürich: Bibl. Inst. 1979.Google Scholar
3. Smith, R. A. and Subbarao, M. V., The average number of divisors in an arithmetic progression, Canad. Math. Bull. 24 (1981), 37-41.10.4153/CMB-1981-005-3CrossRefGoogle Scholar
4. Titchmarsh, E. C., The theory of the Riemann Zeta-function, Oxford: Clarendon Press 1951.Google Scholar