Hostname: page-component-7479d7b7d-767nl Total loading time: 0 Render date: 2024-07-13T03:31:21.402Z Has data issue: false hasContentIssue false
  • English
  • Français

Divisors of Integers in Arithmetic Progression

Published online by Cambridge University Press:  20 November 2018

P. D. Varbanec  and
P. Zarzycki
P. D. Varbanec
Affiliation:
University of Gdańsk, Department of Mathematics, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
P. Zarzycki
Affiliation:
University of Gdańsk, Department of Mathematics, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let d(n; l, k) be the number of positive divisors of n which lie in the arithmetic progression l mod k. Using the complex integration technique the formula

is proved. This formula holds uniformly in l, k and x satisfying 1 ≦ l ≦ k, (lx)1/2 ≦ k ≦ x1-∊; the exponent α ≦ 1/3.

Keywords

11N3711M3511M41
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 129 - 134
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Smith, R. A., Subbarao, M. V., The average number of divisors in an arithmetic progression, Canad. Math. Bull. 24 (1981), 37–41.Google Scholar
2. Nowak, W. G., On a result of Smith and Subbarao concerning a divisor problem, Canad. Math. Bull. 27 (1984), 501–504.Google Scholar
3. Fedoruk, M. V., Saddle-point method, Moscow (1977) (in Russian).Google Scholar
4. Titchmarsh, E. C., The theory of the Riemann zeta-function, Oxford (1951).Google Scholar
5. Kolesnik, G. A., On the estimation of some exponential sums, Acta Arith., XXV (1973), 7–30.Google Scholar
6. Kolesnik, G. A., On the order o/C((l/2) + it) and A(R), Pacific J. Math. 98 (1982), 107–122.Google Scholar