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Some new hybrid power mean formulae of trigonometric sums [PDF]

Advances in Difference Equations, 2020
We apply the analytic method and the properties of the classical Gauss sums to study the computational problem of a certain hybrid power mean of the trigonometric sums and to prove several new mean value formulae for them.
Li Chen, Zhuoyu Chen
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On the Fourth Hybrid Power Mean Involving the Generalized Gauss Sums [PDF]

Journal of Mathematics, 2023
In this paper, we use the elementary and analytic methods to study the fourth hybrid power mean involving the generalized Gauss sums and prove several interesting identities for them.
Xiaoge Liu, Yuanyuan Meng
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One Kind New Hybrid Power Mean and Its Computational Formulae [PDF]

Journal of Mathematics, 2022
The main purpose of this study is to use the elementary and analytic methods and the properties of the classical Gauss sums to study the calculation problems of one kind of hybrid power mean involving the quadratic character sums and the two-term ...
Li Wang, Xuexia Wang
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On the hybrid power mean of two kind different trigonometric sums [PDF]

Open Mathematics, 2019
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 ...
Zhuoyu Chen, Wenpeng Zhang
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On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums [PDF]

Journal of Mathematics, 2021
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 ...
Xiaoling Xu
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The hybrid power mean of the generalized Gauss sums [PDF]

Advances in Difference Equations, 2017
The main purpose of this paper is using the analytic method and the orthogonal properties of the character sums to study the computational problem of one kind hybrid power mean of the generalized Gauss sums mod p $\operatorname{mod}\ p$ , an odd prime ...
Li Chen, Wenpeng Zhang
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On the Hybrid Power Mean of Two-Term Exponential Sums and Cubic Gauss Sums [PDF]

Journal of Mathematics, 2021
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 ...
Shaofan Cao, Tingting Wang
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A note on the hybrid power mean involving the cubic Gauss sums and Kloosterman sums

AIMS Mathematics, 2022
The main purpose of this paper is to study the calculating problem of one kind hybrid power mean involving the cubic Gauss sums and Kloosterman sums, and using the elementary methods, analytic methods and the properties of the classical Gauss sums to ...
Xiaoxue Li , Wenpeng Zhang
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The Hybrid Power Mean of Sixth Gauss Sums and the Two-Term Exponential Sums [PDF]

Journal of Applied Mathematics
The principal aim of this paper is to analyze the hybrid power mean value of sixth Gauss sums and two-term exponential sums. It will use various analytic methods and elementary methods to develop unique identities for these types of sums.
Xuan Wang
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The hybrid power mean of quartic Gauss sums and Kloosterman sums

Open Mathematics, 2017
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 ...
Xiaoxue Li, Jiayuan Hu
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