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
Hauptverfasser: Varbanets, S., Vorobyov, Y.
Format: Artikel
Sprache:Englisch
Veröffentlicht: 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
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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 \(q\), \(q\ll{x}^{\frac{2}{3}-\varepsilon}\).
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institution Algebra and Discrete Mathematics
language English
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publisher Lugansk National Taras Shevchenko University
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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