Norm of Gaussian integers in arithmetical progressions and narrow sectors
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}^{\...
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| Date: | 2020 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2020
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1529 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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 \(q\), \(q\ll{x}^{\frac{2}{3}-\varepsilon}\). |
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