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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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2020
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| Online Zugang: | 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| _version_ | 1856543239822114816 |
|---|---|
| author | Varbanets, S. Vorobyov, Y. |
| author_facet | Varbanets, S. Vorobyov, Y. |
| author_sort | Varbanets, S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-07-08T07:13:20Z |
| 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 \(q\), \(q\ll{x}^{\frac{2}{3}-\varepsilon}\). |
| first_indexed | 2025-12-02T15:30:20Z |
| format | Article |
| id | admjournalluguniveduua-article-1529 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:20Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | 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 |
| 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 |
| title | 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_short | Norm of Gaussian integers in arithmetical progressions and narrow sectors |
| title_sort | norm of gaussian integers in arithmetical progressions and narrow sectors |
| topic | Gaussian integers norm groups Hecke \(Z\)-function functional equation 11L07 11T23 |
| topic_facet | Gaussian integers norm groups Hecke \(Z\)-function functional equation 11L07 11T23 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1529 |
| work_keys_str_mv | AT varbanetss normofgaussianintegersinarithmeticalprogressionsandnarrowsectors AT vorobyovy normofgaussianintegersinarithmeticalprogressionsandnarrowsectors |