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Publications Influence

On the quartic Gauss sums and their recurrence property

- Shimeng Shen, W. Zhang
- Mathematics
- 7 February 2017

The main purpose of this paper is, using the method of trigonometric sums and the properties of Gauss sums, to study the computational problem of one kind of congruence equation modulo an odd prime… Expand

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Some Types of Identities Involving the Legendre Polynomials

- Shimeng Shen, L. Chen
- Mathematics
- 22 January 2019

In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the… Expand

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On Chebyshev polynomials and their applications

- Xingxing Lv, Shimeng Shen
- Mathematics
- 1 December 2017

The main purpose of this paper is, using some properties of the Chebyshev polynomials, to study the power sum problems for the sinx and cosx functions and to obtain some interesting computational… Expand

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Bernoulli Polynomials and Their Some New Congruence Properties

- Ran Duan, Shimeng Shen
- Mathematics, Computer Science
- Symmetry
- 11 March 2019

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The Euler numbers and recursive properties of Dirichlet L-functions

- Yiwei Hou, Shimeng Shen
- Mathematics
- 1 December 2018

The aim of this paper is using an elementary method and the properties of the Bernoulli polynomials to establish a close relationship between the Euler numbers of the second kind En∗$E_{n}^{*}$ and… Expand

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

- Shimeng Shen
- Mathematics
- 1 January 2018

Abstract The 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… Expand

The Generalized Quadratic Gauss Sum and Its Fourth Power Mean

- Shimeng Shen, W. Zhang
- Mathematics
- 12 March 2019

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… Expand

A note on the fourth power mean of the generalized Kloosterman sums

- W. Zhang, Shimeng Shen
- Mathematics
- 1 May 2017

Abstract In the paper [1] , the first author used the analytic methods and the properties of Gauss sums to study the computational problem of the fourth power mean of the generalized Kloosterman sums… Expand

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