Hybrid power mean of 2kth power inversion of L-functions, trigonometric sums and general quartic Gauss sums

2020 ◽  
Vol 66 (9) ◽  
pp. 176-191
Author(s):  
Shikha Singh ◽  
Jagmohan Tanti
Keyword(s):  
Gauss Sums ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Hybrid Power ◽  
Power Inversion ◽  
Hybrid Power Mean

scholarly journals On the Hybrid Power Mean of Two-Term Exponential Sums and Cubic Gauss Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shaofan Cao ◽  
Tingting Wang
Keyword(s):  
Exponential Sums ◽  
Recurrence Formula ◽  
Gauss Sums ◽  
Linear Recurrence ◽  
Power Mean ◽  
Third Order ◽  
Trigonometric Sums ◽  
Order Linear ◽  
Hybrid Power ◽  
Hybrid Power Mean

In this paper, an interesting third-order linear recurrence formula is presented by using elementary and analytic methods. This formula is concerned with the calculating problem of the hybrid power mean of a certain two-term exponential sums and the cubic Gauss sums. As an application of this result, some exact computational formulas for one kind hybrid power mean of trigonometric sums are obtained.

scholarly journals On the hybrid power mean of two kind different trigonometric sums

2019 ◽  
Vol 17 (1) ◽  
pp. 519-526
Author(s):  
Chen Zhuoyu ◽  
Zhang Wenpeng
Keyword(s):  
Gauss Sums ◽  
Analytic Method ◽  
Computational Formula ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Computational Problem ◽  
Hybrid Power ◽  
Hybrid Power Mean

Abstract The main purpose of this paper is using the analytic method, the properties of trigonometric sums and Gauss sums to study the computational problem of one kind hybrid power mean involving two different trigonometric sums, and give an interesting computational formula for it.

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

scholarly journals The hybrid power mean of some special character sums of polynomials and two-term exponential sums modulo $ p $

2021 ◽  
Vol 6 (10) ◽  
pp. 10989-11004
Author(s):  
Wenpeng Zhang ◽  
◽  
Jiafan Zhang ◽  
Keyword(s):  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Analytic Method ◽  
Power Mean ◽  
Hybrid Power ◽  
Special Character ◽  
Modulo P ◽  
Hybrid Power Mean

<abstract><p>We consider the calculation problem of one kind hybrid power mean involving the character sums of polynomials and two-term exponential sums modulo $ p $, an odd prime, and use the analytic method and the properties of classical Gauss sums to give some identities and asymptotic formulas for them.</p></abstract>

scholarly journals On the two-term exponential sums and character sums of polynomials

2019 ◽  
Vol 17 (1) ◽  
pp. 1239-1248
Author(s):  
Yuankui Ma ◽  
Wenpeng Zhang
Keyword(s):  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

Abstract The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character sums of polynomials and two-term exponential sums modulo p, an odd prime, and acquire several accurate asymptotic formulas for them.

scholarly journals A Hybrid Power Mean Involving the Dedekind Sums and Cubic Gauss Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jiayuan Hu ◽  
Yu Zhan ◽  
Qin Si
Keyword(s):  
Gauss Sums ◽  
Gauss Sum ◽  
Dedekind Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

The main purpose of this paper is using analytic methods and the properties of the Dedekind sums to study one kind hybrid power mean calculating problem involving the Dedekind sums and cubic Gauss sum and give some interesting calculating formulae for it.

scholarly journals On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Xiaoling Xu
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Dedekind Sums ◽  
Character Sum ◽  
Kloosterman Sum ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

The main purpose of this paper is to use the elementary and analytic methods, the properties of Gauss sums, and character sums to study the computational problem of a certain hybrid power mean involving the Dedekind sums and a character sum analogous to Kloosterman sum and give two interesting identities for them.

scholarly journals The hybrid power mean of quartic Gauss sums and Kloosterman sums

2017 ◽  
Vol 15 (1) ◽  
pp. 151-156 ◽  
Author(s):  
Li Xiaoxue ◽  
Hu Jiayuan
Keyword(s):  
Gauss Sums ◽  
Kloosterman Sums ◽  
Analytic Method ◽  
Computational Formula ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Hybrid Power Mean

Abstract The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact computational formula for it.

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