scholarly journals On a Certain Quadratic Character Sums of Ternary Symmetry Polynomials mod p

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yuanyuan Meng
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Quadratic Character ◽  
Elementary Methods ◽  
Mod P

In this article, we are using the elementary methods and the properties of the classical Gauss sums to study the calculating problem of a certain quadratic character sums of a ternary symmetry polynomials modulo p and obtain some interesting identities for them.

scholarly journals The Mean Values of Character Sums and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 318
Author(s):  
Jiafan Zhang ◽  
Yuanyuan Meng
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Mean Values ◽  
Special Polynomials ◽  
Elementary Methods ◽  
The Mean

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.

scholarly journals A Note on the Classical Gauss Sums

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 313 ◽  
Author(s):  
Tingting Wang ◽  
Guohui Chen
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Algebraic Methods ◽  
Computational Problem ◽  
Exact Evaluation ◽  
Rational Polynomials ◽  
Mod P

The main purpose of this paper is to study the computational problem of one kind rational polynomials of the classical Gauss sums, and using the purely algebraic methods and the properties of the character sums mod p ( a prime with p ≡ 1 mod 12 ) to give an exact evaluation formula for it.

The Quadratic Character of 2 mod p

1976 ◽  
Vol 49 (2) ◽  
pp. 89-90
Author(s):  
Kenneth S. Williams
Keyword(s):  
Quadratic Character ◽  
Mod P

scholarly journals On Classical Gauss Sums and Some of Their Properties

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 625 ◽  
Author(s):  
Li Chen
Keyword(s):  
Recursive Formula ◽  
Character Sums ◽  
Gauss Sums ◽  
Computational Problem ◽  
Rational Polynomials

The goal of this paper is to solve the computational problem of one kind rational polynomials of classical Gauss sums, applying the analytic means and the properties of the character sums. Finally, we will calculate a meaningful recursive formula for it.

scholarly journals The Quadratic Residues and Some of Their New Distribution Properties

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 421 ◽  
Author(s):  
Tingting Wang ◽  
Xingxing Lv
Keyword(s):  
Counting Function ◽  
Character Sums ◽  
Asymptotic Formulas ◽  
Open Problems ◽  
Quadratic Residues ◽  
New Distribution ◽  
Mod P

In this paper, we give some interesting identities and asymptotic formulas for one kind of counting function, by studying the computational problems involving the symmetry sums of one kind quadratic residues and quadratic non-residues mod p . The main methods we used are the properties of the Legendre’s symbol mod p , and the estimate for character sums. As application, we solve two open problems proposed by Zhiwei Sun.

scholarly journals The generalized quadratic Gauss sums and its sixth power mean

2021 ◽  
Vol 6 (10) ◽  
pp. 11275-11285
Author(s):  
Xingxing Lv ◽  
◽  
Wenpeng Zhang
Keyword(s):  
Gauss Sums ◽  
Power Mean ◽  
Computational Problem ◽  
Elementary Methods

<abstract><p>In this article, we using elementary methods, the number of the solutions of some congruence equations and the properties of the Legendre's symbol to study the computational problem of the sixth power mean of a certain generalized quadratic Gauss sums, and to give an exact calculating formula for it.</p></abstract>

scholarly journals A hybrid mean value of the inversion of L-functions and general quadratic Gauss sums

2002 ◽  
Vol 167 ◽  
pp. 1-15 ◽  
Author(s):  
Wenpeng Zhang ◽  
Yuping Deng
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Analytic Method ◽  
Power Mean ◽  
Hybrid Mean Value

AbstractThe main purpose of this paper is, using the estimates for character sums and the analytic method, to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums, and give two interesting asymptotic formulas.

scholarly journals On the fourth-order linear recurrence formula related to classical Gauss sums

2017 ◽  
Vol 15 (1) ◽  
pp. 1251-1255 ◽  
Author(s):  
Chen Zhuoyu ◽  
Zhang Wenpeng
Keyword(s):  
Positive Integer ◽  
Fourth Order ◽  
Recurrence Formula ◽  
Character Sums ◽  
Gauss Sums ◽  
Linear Recurrence ◽  
Analytic Method ◽  
Order Linear ◽  
Computational Problem

Abstract Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recurrence formula for it, where τ(ψ) denotes the classical Gauss sums.

scholarly journals The Generalized Quadratic Gauss Sum and Its Fourth Power Mean

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 258
Author(s):  
Shimeng Shen ◽  
Wenpeng Zhang
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Gauss Sum ◽  
Fourth Power ◽  
Power Mean ◽  
Analytic Methods ◽  
Fourth Power Mean

In this article, our main purpose is to introduce a new and generalized quadratic Gauss sum. By using analytic methods, the properties of classical Gauss sums, and character sums, we consider the calculating problem of its fourth power mean and give two interesting computational formulae for it.

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