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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
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Abstract

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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

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