Divisors of the Gaussian integers in an arithmetic progression
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.
scientific article; zbMATH DE number 4116635