Divisors of the Gaussian integers in an arithmetic progression
type: Item
instance of: scholarly article
title: Divisors of the Gaussian integers in an arithmetic progression
zbMATH Open document ID: 0682.10033
DOI: 10.1016/0022-314X(89)90003-6
author: P. D. Varbanec
author: Piotr Zarzycki
published in: Journal of Number Theory
publication date: 1989-01-01T00:00:00Z
review text: Let \(d(n;\ell,k)\) denote the number of divisors of the natural number \(n\) which are congruent to \(\ell \bmod k\). R. A. Smith and M. V. Subbarao proved an asymptotic result for the summatory function which was improved by \textit{W. G. Nowak} [Can. Math. Bull. 27, 501--504 (1984; Zbl 0519.10033)]. The authors investigate in this paper the number of divisors \(d(\omega;\alpha,\gamma)\) of the Gaussian integer \(\omega\) which lie in the arithmetic progression \(\alpha\bmod\gamma\). They prove an asymptotic result for the summatory function of the quality of Nowak's result.
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11N13
Mathematics Subject Classification ID: 11R04
zbMATH DE Number: 4116635
zbMATH Keywords: number of divisors
zbMATH Keywords: Gaussian integer
zbMATH Keywords: arithmetic progression
zbMATH Keywords: asymptotic result
zbMATH Keywords: summatory function
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
cites work: Q5554455
cites work: Topics in multiplicative number theory
cites work: On a Result of Smith and Subbarao Concerning a Divisor Problem
cites work: Q3248054
cites work: The Average Number of Divisors in an Arithmetic Progression
cites work: The zeros of the Riemann zeta-function
full work available at URL: 0022-314x(89)90003-6
OpenAlex ID: W2002283863
description: scientific article; zbMATH DE number 4116635