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A New Sum Analogous to Gauss Sums and Its Fourth Power Mean [PDF]
The Scientific World Journal, 2014 The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate ...
Shaofeng Ru, Wenpeng Zhang
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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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Polyhedral Gauss sums, and polytopes with symmetry
Journal of Computational Geometry, 2016 We define certain natural finite sums of $n$'th roots of unity, called $G_P(n)$, that are associated to each convex integer polytope $P$, and which generalize the classical $1$-dimensional Gauss sum $G(n)$ defined over $\mathbb Z/ {n \mathbb Z}$, to ...
Romanos Diogenes Malikiosis +2 more
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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 \(\mathbf{e}_{p}(z)=\exp (2 \pi i z / p)\).
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One-Kind Hybrid Power Means of the Two-Term Exponential Sums and Quartic Gauss Sums
Journal of Mathematics, 2021 The main purpose of this article is using the analytic methods and the properties of the classical Gauss sums to study the calculating problem of the hybrid power mean of the two-term exponential sums and quartic Gauss sums and then prove two interesting
Xiaoxue Li, Li Chen
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Journal of Mathematics, 2021 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 hybrid power mean involving the quartic Gauss sums and two-term exponential sums and give an ...
Lan Qi, Xingxing Lv
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Journal of Mathematics, 2021 In this paper, we use the analytic methods and the properties of the classical Gauss sums to study the properties of the error term of the fourth power mean of the generalized cubic Gauss sums and give two recurrence formulae for it.
Zhang Jin, Zhang Jiafan
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Some new hybrid power mean formulae of trigonometric sums
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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Proceedings of the American Mathematical Society, 2005 Let \(p\) be a prime number, \(\theta\) be a nonzero element of the finite field \(\mathbb F_p\) of multiplicative order \(t \geq 1\), and let \(\mathcal Z = \{z_1, z_2, \dots, z_T\}\) be a sequence of elements of \(\mathbb Z / t\mathbb Z\). Given two polynomials \(f(X), g(X) \in \mathbb F_p[X]\), an additive character \(\psi\) of \(\mathbb F_p\), and ...
Cohen, Stephen D. +4 more
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Evaluations of a Weighted Average of Gauss Sums
Journal of Mathematics, 2021 In this paper, we perform a further investigation for a weighted average of Gauss sums. By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the ...
Wen-Kai Shao, Yuan He
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