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 A Four-Order Linear Recurrence Formula Involving the Quartic Gauss Sums and One Kind Two-Term Exponential Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lan Qi ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Recurrence Formula ◽  
Gauss Sums ◽  
Linear Recurrence ◽  
Analytic Method ◽  
Power Mean ◽  
Order Linear ◽  
Hybrid Power ◽  
Hybrid Power Mean ◽  
Mathematica Software

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 hybrid power mean involving the quartic Gauss sums and two-term exponential sums and give an interesting four-order linear recurrence formula for it. As an application, we can obtain all values of this kind hybrid power mean with mathematica software.

scholarly journals On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums

2018 ◽  
Vol 16 (1) ◽  
pp. 955-966
Author(s):  
Shimeng Shen
Keyword(s):  
Exponential Sums ◽  
Gauss Sums ◽  
Linear Recurrence ◽  
Analytic Method ◽  
Computational Formula ◽  
Power Mean ◽  
Hybrid Power ◽  
Recurrence Formulae ◽  
Hybrid Power Mean ◽  
Congruence Equation

AbstractThe main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some interesting fourth-order linear recurrence formulae for this problem. As an application of our result, we can also obtain an exact computational formula for one kind congruence equation modp, an odd prime.

scholarly journals One-Kind Hybrid Power Means of the Two-Term Exponential Sums and Quartic Gauss Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xiaoxue Li ◽  
Li Chen
Keyword(s):  
Exponential Sums ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Linear Recurrence ◽  
Power Mean ◽  
Hybrid Power ◽  
Recurrence Formulas ◽  
Analytic Methods ◽  
Power Means ◽  
Hybrid Power Mean

The main purpose of this article is using the analytic methods and the properties of the classical Gauss sums to study the calculating problem of the hybrid power mean of the two-term exponential sums and quartic Gauss sums and then prove two interesting linear recurrence formulas. As applications, some asymptotic formulas are obtained.

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 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 The character sum of polynomials with k variables and two-term exponential sums

2021 ◽  
Vol 27 (1) ◽  
pp. 112-124
Author(s):  
Xiaoling Xu ◽  
◽  
Jiafan Zhang ◽  
Wenpeng Zhang ◽  
◽  
...  
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Character Sum ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

The main purpose of this paper is using the properties of the classical Gauss sums and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sums of polynomials with k variables and the two-term exponential sums, and give an identity and asymptotic formula for it.

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