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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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Identities on quadratic Gauss sums [PDF]

Transactions of the American Mathematical Society, 1990
Given a local field F F , each multiplicative character θ \theta of the split algebra F × F F \times F or of a separable quadratic extension of F F has an associated generalized Gauss sum γ θ F \gamma _\theta ^F .
Paul Gérardin, Wen-Ching Winnie Li
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On quadratic Gauss sums and variations thereof [PDF]

Cogent Mathematics, 2015
A number of new terminating series involving $\sin(n^2/k)$ and $\cos(n^2/k)$ are presented and connected to Gauss quadratic sums. Several new closed forms of generic Gauss quadratic sums are obtained and previously known results are generalized.
M. L. Glasser, Michael Milgram
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On a rigidity property for quadratic Gauss sums [PDF]

Mathematika
Abstract Let be a large prime and let . We prove that if is a ‐valued multiplicative function, such that the exponential sums satisfy the ‘Gauss sum‐like’ approximate dilation symmetry property uniformly over all primes , then ...
Alexander P. Mangerel
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On some conjectures on Generalized quadratic Gauss sums and related problems [PDF]

Finite Fields and Their Applications, 2021
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, Antonio Rojas‐León, Wenpeng Zhang   +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.
Nilanjan Bag, Rupam Barman
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On the structure of quadratic Gauss sums in the Talbot effect [PDF]

Journal of the Optical Society of America A, 2017
We report on the detailed derivation of the Gauss sums leading to the weighting phase factors in the fractional Talbot effect. In contrast to previous approaches, the derivation is directly based on the two coprime integers p and q that define the fractional Talbot effect so that, using standard techniques from the number theory, the computation is ...
Carlos R. Fernández‐Pousa
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Equientangled Bases in Arbitrary Dimensions and Quadratic Gauss Sums [PDF]

, 2010
This paper has been withdrawn due to the submission of a major revised version, arXiv:1004.1633 [quant-ph]. The latter provides an additional solution and contains significantly new material.
Vlad Gheorghiu
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Note on the quadratic Gauss sums [PDF]

International Journal of Mathematics and Mathematical Sciences, 2001
Let p be an odd prime and {χ(m) = (m/p)}, m = 0, 1, …, p − 1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ  modp which are defined in terms of the Legendre symbol (m/p), (m, p) = 1. We study the relation between the Gauss and the quadratic Gauss sums.
George Danas
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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.
Jia an Zhang, Xingx ng Lv
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