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Algebra and Discrete Mathematics, 2020, Volume 29, Issue 2, Pages 259–270
DOI: https://doi.org/10.12958/adm1529
(Mi adm757)
 

RESEARCH ARTICLE

Norm of Gaussian integers in arithmetical progressions and narrow sectors

S. Varbanetsa, Ya. Vorobyovb

a Odessa I.I. Mechnikov National University, Dvoryanskaya str. 2, 65026 Odessa, Ukraine
b Izmail State Humanities University, Izmail, Repina str. 12, 68610 Izmail, Ukraine
References:
Abstract: 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 $q$, $q\ll{x}^{\frac{2}{3}-\varepsilon}$.
Keywords: Gaussian integers, norm groups, Hecke $Z$-function, functional equation.
Received: 20.01.2020
Bibliographic databases:
Document Type: Article
MSC: 11L07, 11T23
Language: English
Citation: S. Varbanets, Ya. Vorobyov, “Norm of Gaussian integers in arithmetical progressions and narrow sectors”, Algebra Discrete Math., 29:2 (2020), 259–270
Citation in format AMSBIB
\Bibitem{VarVor20}
\by S.~Varbanets, Ya.~Vorobyov
\paper Norm of Gaussian integers in arithmetical progressions and narrow sectors
\jour Algebra Discrete Math.
\yr 2020
\vol 29
\issue 2
\pages 259--270
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\crossref{https://doi.org/10.12958/adm1529}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087573482}
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