RESEARCH ARTICLE

Quadratic residues of the norm group in sectorial domains

Lyubov Balyas, Pavel Varbanets

I. I. Mechnikov Odessa National University

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.

MSC: 11L05, 11L07, 11N25, 11S40

Received: 29.01.2016
Revised: 29.12.2016

Language: English

Bibliographic databases:

• 
•