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The generalized quadratic Gauss sums and its sixth power mean
AIMS Mathematics, 2021 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 ...
Xingxing Lv, Wenpeng Zhang
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The Generalized Quadratic Gauss Sum and Its Fourth Power Mean [PDF]
Mathematics, 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 calculating problem of its fourth power mean and give two ...
Shimeng Shen, Wenpeng Zhang
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Generalized quadratic Gauss sums and their 2mth power mean
Open MathematicsThe main purpose of this article is to study the problem of calculating the 2mth power mean of the generalized quadratic Gauss sums, and using the analytic method and an interesting combinatorial identity to give a sharp asymptotic formula for the 2mth ...
Cui Dewang, Zhang Wenpeng
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AIMS MathematicsIn this paper, the fourth power mean values of the generalized quadratic Gauss sums associated with the $ 3 $-order and $ 4 $-order Dirichlet characters are given by using the properties of the Dirichlet characters and Gauss sums.
Xuan Wang, Li Wang , Guohui Chen
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On some conjectures on generalized quadratic Gauss sums and related problems [PDF]
Finite Fields and Their Applications, 2023 The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which were proposed in \cite{BLZ}.
Nilanjan Bag +2 more
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Higher order moments of generalized quadratic Gauss sums weighted by $L$-functions [PDF]
Asian Journal of Mathematics, 2021 The main purpose of this paper is to study higher order moments of the generalized quadratic Gauss sums weighted by $L$-functions using estimates for character sums and analytic methods. We find asymptotic formulas for three character sums which arise naturally in the study of higher order moments of the generalized quadratic Gauss sums.
Bag, Nilanjan, Barman, Rupam
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On the generalized quadratic Gauss sums and its upper bound estimate [PDF]
Journal of Mathematical Inequalities, 2021 Summary: The main purpose of this paper is to study generalized quadratic Gauss sums, then use the analytic methods, the properties of the classical Gauss sums and character sums to give a sharp upper bound estimate for it. In addition, we also give several interesting fourth and sixth power mean formulae for the sums.
Zhang, Jiafan, Lv, Xingxing
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Moments of Generalized Quadratic Gauss Sums Weighted by L-Functions
Journal of Number Theory, 2002 The author studies moments of the generalized quadratic Gauss sum \[ G(n, \chi; q)=\sum_{a=1}^q\chi(a)\exp(2\pi ina^2/q),\;q,n\in\mathbb Z,\;q\geq 2, \] weighted by the Dirichlet \(L\)-function \(L(s, \chi)\), where \(\chi\) is the character modulo \(q\). Let \(p\) denote an odd prime and let \((n, p)=1\).
Wenpeng Zhang
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ON THE 2k-TH POWER MEAN VALUE OF THE GENERALIZED QUADRATIC GAUSS SUMS [PDF]
Bulletin of the Korean Mathematical Society, 2011 Abstract. The main purpose of this paper is using the elementary andanalytic methods to study the properties of the 2 k -th power mean valueof the generalized quadratic Gauss sums, and give two exact mean valueformulae for k = 3 and 4. 1. IntroductionLet q 2 be an integer, ˜ denotes a Dirichlet character modulo q .
Yanfeng He, Wenpeng Zhang
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On the 1-error linear complexity of two-prime generator
AIMS Mathematics, 2022 Jing et al. dealed with all possible Whiteman generalized cyclotomic binary sequences $ s(a, b, c) $ with period $ N = pq $, where $ (a, b, c) \in \{0, 1\}^3 $ and $ p, q $ are distinct odd primes (Jing et al. arXiv:2105.10947v1, 2021).
Tongjiang Yan +2 more
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