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Algebra and Discrete Mathematics, 2016, Volume 22, Issue 2, Pages 153–170 (Mi adm580)  
RESEARCH ARTICLE

Quadratic residues of the norm group in sectorial domains

Lyubov Balyas, Pavel Varbanets

I. I. Mechnikov Odessa National University
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Abstract: In the article the distribution of quadratic residues in the ring $G_{p^n}$, in the norm subgroup $E_n$ of multiplicative group $G_{p^n}^{*}$, is investigated. The asymptotic formula for the number $R(x,\phi)$ of quadratic residues in the sectorial domain of a special form has been constructed.
Keywords: quadratic residue, the norm group, Hecke Z-function, the gamma function, Dirichlet series, functional equation, Gaussian integers.
Received: 29.01.2016
Revised: 29.12.2016
Bibliographic databases:
Document Type: Article
MSC: 11L05, 11L07, 11N25, 11S40
Language: English
Citation: Lyubov Balyas, Pavel Varbanets, “Quadratic residues of the norm group in sectorial domains”, Algebra Discrete Math., 22:2 (2016), 153–170
Citation in format AMSBIB
\Bibitem{BalVar16}
\by Lyubov~Balyas, Pavel~Varbanets
\paper Quadratic residues of the norm group in~sectorial domains
\jour Algebra Discrete Math.
\yr 2016
\vol 22
\issue 2
\pages 153--170
\mathnet{http://mi.mathnet.ru/adm580}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3593117}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000392709600001}
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