Results 11 to 20 of about 40,388 (276)
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
doaj +2 more sources
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
core +2 more sources
Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits [PDF]
Quantum, 2021 One of the lowest-order corrections to Gaussian quantum mechanics in infinite-dimensional Hilbert spaces are Airy functions: a uniformization of the stationary phase method applied in the path integral perspective.
Lucas Kocia, Peter Love
doaj +4 more sources
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
doaj +2 more sources
On the High-Power Mean of the Generalized Gauss Sums and Kloosterman Sums
Mathematics, 2019 The main aim of this paper is to use the properties of the trigonometric sums and character sums, and the number of the solutions of several symmetry congruence equations to research the computational problem of a certain sixth power mean of the ...
Xinyu Liu, Wenpeng Zhang
doaj +3 more sources
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
doaj +4 more sources
On the fourth-order linear recurrence formula related to classical Gauss sums
Open Mathematics, 2017 Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ ...
Zhuoyu Chen, Wenpeng Zhang
doaj +2 more sources
A Note on the Classical Gauss Sums
Mathematics, 2018 The main purpose of this paper is to study the computational problem of one kind rational polynomials of the classical Gauss sums, and using the purely algebraic methods and the properties of the character sums mod p (a prime with p ≡
Tingting Wang, Guohui Chen
doaj +3 more sources
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 \(\mathbf{e}_{p}(z)=\exp (2 \pi i z / p)\).
openaire +2 more sources
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
doaj +1 more source