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Bilinear sums of Gauss sums [PDF]
Acta Arithmetica, 2022 Let \(p \geq 3\) be a prime number. Motivated by results on bilinear sums of Kloosterman sums and their generalisations, the author considers sums with Gauss sums \[ G(m, n)=\sum_{x=1}^{p} \mathbf{e}_{p}\left(m x+n x^{2}\right), \] where \(\mathbf{e}_{p}(z)=\exp (2 \pi i z / p)\).
I. Shparlinski
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On the classical Gauss sums and their some new identities
AIMS Mathematics, 2022 In this paper, we use the analytic methods and the properties of the classical Gauss sums to study the calculating problems of some Gauss sums involving the character of order $ 12 $ modulo an odd prime $ p $, and obtain several new and interesting ...
Wenpeng Zhang, Xiaodan Yuan
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Gauss Sums and Quantum Mechanics [PDF]
Journal of Physics A: Mathematical and General, 2000 By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given.
Alice Rogers +13 more
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Higher Gauss sums of modular categories [PDF]
Selecta Mathematica, 2019 The definitions of the $n^{th}$ Gauss sum and the associated $n^{th}$ central charge are introduced for premodular categories $\mathcal{C}$ and $n\in\mathbb{Z}$. We first derive an expression of the $n^{th}$ Gauss sum of a modular category $\mathcal{C}$,
Ng, Siu-Hung +2 more
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Incomplete Gauss sums modulo primes [PDF]
The Quarterly Journal of Mathematics, 2017 . We obtain a new bound for incomplete Gauss sums modulo primes. Our argument falls under the framework of Vinogradov’s method which we use to reduce the problem under consideration to bounding the number of solutions to two distinct systems of ...
Bryce Kerr
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On sums of Kloosterman and Gauss sums
Transactions of the American Mathematical Society, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
I. Shparlinski
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Gauss sums and Van der Geer–Van der Vlugt curves [PDF]
Bulletin of the London Mathematical Society, 2023 We study Van der Geer–Van der Vlugt curves in a ramification‐theoretic view point. We give explicit formulae on the L$L$ ‐polynomials of these curves.
Daichi Takeuchi, Takahiro Tsushima
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Gauss sums and the maximum cliquesin generalized Paley graphs of square order [PDF]
Functiones et Approximatio Commentarii Mathematici, 2021 Let GP (q, d) be the d-Paley graph defined on the finite field Fq . It is notoriously difficult to improve the trivial upper bound √ q on the clique number of GP (q, d).
Chi Hoi Yip
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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.
Nilanjan Bag, Rupam Barman
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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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