Divisor function of the Gaussian integers weighted by the Kloosterman sum

• Date: 2026
• Main Authors: Varbanets, Pavel, Varbanets, Sergey, Vorobyov, Yakov
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: exponential sums; Kloosterman sums; asymptotic formulas; divisor function; 11L05; 11L07
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2436
• Journal Title: Algebra and Discrete Mathematics

We study the mean values of the divisor function \(\tau(\omega)\) over the ring of Gaussian integers \(G\) when weighted by Kloosterman sums. For \(\alpha,\beta,\gamma\in{G}\) with \(\gamma\neq0\), let \(K(\alpha,\beta;\gamma)=\sum\limits_{x\in{G}_\gamma^\ast}\exp\left(2\pi{i}\Re\left(\frac{\alpha{x...