Results 11 to 20 of about 164,472 (335)
A remark for Gauss sums of order 3 and some applications for cubic congruence equations
AIMS Mathematics, 2022 In this paper, we give some relations between Gauss sums of order 3. As application, we give the number of solutions of some cubic diagonal equations. These generalize the earlier results obtained by Hong-Zhu and solve the sign problem raised by Zhang ...
Wenxu Ge, Weiping Li, Tianze Wang
doaj +1 more source
On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums
Journal of Mathematics, 2021 The main purpose of this paper is to use the elementary and analytic methods, the properties of Gauss sums, and character sums to study the computational problem of a certain hybrid power mean involving the Dedekind sums and a character sum analogous to ...
Xiaoling Xu
doaj +1 more source
The number of rational points of certain quartic diagonal hypersurfaces over finite fields
AIMS Mathematics, 2020 Let $p$ be an odd prime and let $\mathbb{F}_q$ be a finite field of characteristic $p$ with order $q=p^s$. For $f(x_1, \cdots, x_n)\in\mathbb{F}_q[x_1, ..., x_n]$, we denote by $N(f(x_1, \cdots, x_n)=0)$ the number of $\mathbb{F}_q$-rational points on ...
Junyong Zhao, Shaofang Hong, Chaoxi Zhu
doaj +1 more source
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. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved.
Armitage, Vernon, Rogers, Alice
openaire +2 more sources
A Hybrid Power Mean Involving the Dedekind Sums and Cubic Gauss Sums
Journal of Mathematics, 2021 The main purpose of this paper is using analytic methods and the properties of the Dedekind sums to study one kind hybrid power mean calculating problem involving the Dedekind sums and cubic Gauss sum and give some interesting calculating formulae for it.
Jiayuan Hu, Yu Zhan, Qin Si
doaj +1 more source
On the number of solutions of two-variable diagonal quartic equations over finite fields
AIMS Mathematics, 2020 Let $p$ be a odd prime number and let $\mathbb{F}_q$ be the finite field of characteristic $p$ with $q$ elements. In this paper, by using the Gauss sum and Jacobi sum, we give an explicit formula for the number $N(x_1^4+x_2^4=c)$ of solutions of the ...
Junyong Zhao, Yang Zhao, Yujun Niu
doaj +1 more source
Fourth power mean values of one kind special Kloosterman's sum
Electronic Research Archive, 2023 The main purpose of this article is using the analytic methods and properties of classical Gauss sums to study the calculating problem of fourth power mean values of one kind special Kloosterman's sum, and give a sharp asymptotic formula for it.
Li Rui, Nilanjan Bag
doaj +1 more source
Higher Gauss sums of modular categories [PDF]
, 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
core +3 more sources
On the classical Gauss sum and the recursive properties
Advances in Difference Equations, 2018 Let p be a prime with p≡1mod8 $p\equiv1\bmod8$, ψ be an eighth character modp, and τ(ψ) $\tau(\psi)$ denote the classical Gauss sum modp. The main purpose of this paper is using the analytic method and the properties of the classical Gauss sum to study ...
Hui Bai, Jiayuan Hu
doaj +1 more source
The quantum-mechanical Coulomb propagator in an L2 function representation
Scientific Reports, 2021 The quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated.
Rolf Gersbacher, John T. Broad
doaj +1 more source