Norm of Gaussian integers in arithmetical progressions and narrow sectors

• Date: 2020
• Main Authors: Varbanets, S., Vorobyov, Y.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: Gaussian integers; norm groups; Hecke \(Z\)-function; functional equation; 11L07; 11T23
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1529
• Journal Title: Algebra and Discrete Mathematics

We proved the equidistribution of the Gaussian integer numbers in narrow sectors of the circle of radius \(x^{\frac{1}{2}}\), \(x\to\infty\), with the norms belonging to arithmetic progression \(N(\alpha)\equiv\ell\pmod{q}\) with the common difference of an arithmetic progression \(q\), \(q\ll{x}^{\...