scholarly journals Some Symmetric Identities Involving Fubini Polynomials and Euler Numbers

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 303 ◽  
Author(s):  
Zhao Jianhong ◽  
Chen Zhuoyu
Keyword(s):  
Calculation Method ◽  
Computational Formula ◽  
Euler Numbers ◽  
Special Sequence ◽  
Computational Problem ◽  
Elementary Methods ◽  
Symmetric Identities ◽  
Recursive Calculation

The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.

scholarly journals Some Symmetric Identities for the Multiple (p, q)-Hurwitz-Euler eta Function

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 645 ◽  
Author(s):  
Kyung-Won Hwang ◽  
Cheon Seoung Ryoo
Keyword(s):  
Higher Order ◽  
Complex Field ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials ◽  
Symmetric Identities ◽  
Symmetric Properties

The main purpose of this paper is to find some interesting symmetric identities for the ( p , q ) -Hurwitz-Euler eta function in a complex field. Firstly, we define the multiple ( p , q ) -Hurwitz-Euler eta function by generalizing the Carlitz’s form ( p , q ) -Euler numbers and polynomials. We find some formulas and properties involved in Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order. We find new symmetric identities for multiple ( p , q ) -Hurwitz-Euler eta functions. We also obtain symmetric identities for Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order by using symmetry about multiple ( p , q ) -Hurwitz-Euler eta functions. Finally, we study the distribution and symmetric properties of the zero of Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order.

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 On the Sixth Power Mean Value of the Generalized Three-Term Exponential Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Yahui Yu ◽  
Wenpeng Zhang
Keyword(s):  
Exponential Sums ◽  
Mean Value ◽  
Computational Formula ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Computational Problem

The main purpose of this paper is using the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean value of the generalized three-term exponential sums and give an exact computational formula for it.

scholarly journals One kind sixth power mean of the three-term exponential sums

2017 ◽  
Vol 15 (1) ◽  
pp. 705-710 ◽  
Author(s):  
Xiaoying Wang ◽  
Xiaoxue Li
Keyword(s):  
Exponential Sums ◽  
Computational Formula ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Computational Problem

Abstract In this paper, we use the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean of the three-term exponential sums. As a conclusion, we give an exact computational formula for it.

scholarly journals Tribonacci Numbers and Some Related Interesting Identities

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1195 ◽  
Author(s):  
Shujie Zhou ◽  
Li Chen
Keyword(s):  
Power Series ◽  
Computational Problem ◽  
Symmetry Properties ◽  
Elementary Methods ◽  
Tribonacci Numbers

The main purpose of this paper is, by using elementary methods and symmetry properties of the summation procedures, to study the computational problem of a certain power series related to the Tribonacci numbers, and to give some interesting identities for these numbers.

scholarly journals On the General Dedekind Sums and Two-Term Exponential Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Junli Zhang ◽  
Wenpeng Zhang
Keyword(s):  
Exponential Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Dedekind Sums ◽  
Computational Formula ◽  
Computational Problem ◽  
Hybrid Mean Value ◽  
Analytic Methods

We use the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid mean value involving the general Dedekind sums and the two-term exponential sums, and give an interesting computational formula for it.

scholarly journals One kind power mean of the hybrid Gauss sums

2018 ◽  
Vol 16 (1) ◽  
pp. 531-538
Author(s):  
Qi Lan ◽  
Zhang Wenpeng
Keyword(s):  
Exact Formula ◽  
Gauss Sums ◽  
Computational Formula ◽  
Analysis Method ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Number Of Solutions ◽  
Computational Problem ◽  
Congruence Equation

AbstractIn this paper, we use the analysis method and the properties of trigonometric sums to study the computational problem of one kind power mean of the hybrid Gauss sums. After establishing some relevant lemmas, we give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation modp, wherepbe an odd prime.

scholarly journals A Certain Mean Square Value Involving Dirichlet L-Functions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 948
Author(s):  
Wenpeng Zhang ◽  
Di Han
Keyword(s):  
Positive Integer ◽  
Character Sums ◽  
Mean Square ◽  
Trigonometric Sums ◽  
Integer Points ◽  
Computational Problem ◽  
Elementary Methods

The main purpose of this article is using the elementary methods, the properties of Dirichlet L-functions to study the computational problem of a certain mean square value involving Dirichlet L-functions at positive integer points, and give some exact calculating formulae. As some applications, we obtain some interesting identities and inequalities involving character sums and trigonometric sums.

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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