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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| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2020
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1529 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-1529 |
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admjournalluguniveduua-article-15292020-07-08T07:13:20Z Norm of Gaussian integers in arithmetical progressions and narrow sectors Varbanets, S. Vorobyov, Y. Gaussian integers, norm groups, Hecke \(Z\)-function, functional equation 11L07, 11T23 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 \(q\), \(q\ll{x}^{\frac{2}{3}-\varepsilon}\). Lugansk National Taras Shevchenko University 2020-07-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1529 10.12958/adm1529 Algebra and Discrete Mathematics; Vol 29, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1529/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1529/655 Copyright (c) 2020 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2020-07-08T07:13:20Z |
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OJS |
| language |
English |
| topic |
Gaussian integers norm groups Hecke \(Z\)-function functional equation 11L07 11T23 |
| spellingShingle |
Gaussian integers norm groups Hecke \(Z\)-function functional equation 11L07 11T23 Varbanets, S. Vorobyov, Y. Norm of Gaussian integers in arithmetical progressions and narrow sectors |
| topic_facet |
Gaussian integers norm groups Hecke \(Z\)-function functional equation 11L07 11T23 |
| format |
Article |
| author |
Varbanets, S. Vorobyov, Y. |
| author_facet |
Varbanets, S. Vorobyov, Y. |
| author_sort |
Varbanets, S. |
| title |
Norm of Gaussian integers in arithmetical progressions and narrow sectors |
| title_short |
Norm of Gaussian integers in arithmetical progressions and narrow sectors |
| title_full |
Norm of Gaussian integers in arithmetical progressions and narrow sectors |
| title_fullStr |
Norm of Gaussian integers in arithmetical progressions and narrow sectors |
| title_full_unstemmed |
Norm of Gaussian integers in arithmetical progressions and narrow sectors |
| title_sort |
norm of gaussian integers in arithmetical progressions and narrow sectors |
| description |
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 \(q\), \(q\ll{x}^{\frac{2}{3}-\varepsilon}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1529 |
| work_keys_str_mv |
AT varbanetss normofgaussianintegersinarithmeticalprogressionsandnarrowsectors AT vorobyovy normofgaussianintegersinarithmeticalprogressionsandnarrowsectors |
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2025-12-02T15:30:20Z |
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2025-12-02T15:30:20Z |
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1850412049092313089 |