Results 21 to 30 of about 121,729 (283)
Proceedings of the American Mathematical Society, 1956 where p is an odd prime, has been proved in a variety of ways. In particular the proof in [3, p. 623 ] may be cited. We remark that Estermann [1 ] has recently given a simple proof of (1) that is valid for arbitrary odd p. In the present note we indicate a short proof of (1) that makes use of some familiar results from cyclotomy. Let E = e27riP and let
openaire +2 more sources
Gauss Quadrature for Integrals and Sums
International Journal of Pure and Applied Mathematics Research, 2023 Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.
openaire +3 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. 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
Relative norms of Gauss sums [PDF]
, 1987 The explicit determination of the values of Gauss sums is a very classical problem and has some rather deep arithmetic consequences in classfield theory. Here we study the simpler problem of finding their relative norms.
Gurak, S
core +1 more source
The Generalized Quadratic Gauss Sum and Its Fourth Power Mean
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
doaj +1 more source
One Kind New Hybrid Power Mean and Its Computational Formulae
Journal of Mathematics, 2022 The main purpose of this study is to use the elementary and analytic methods and the properties of the classical Gauss sums to study the calculation problems of one kind of hybrid power mean involving the quadratic character sums and the two-term ...
Li Wang, Xuexia Wang
doaj +1 more source
Identities on quadratic Gauss sums [PDF]
Transactions of the American Mathematical Society, 1990 Given a local field F F , each multiplicative character
Paul Gerardin, Wen-Ch' Ing Winnie Li
openaire +1 more source
Gauss sums over some matrix groups [PDF]
, 2012 In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involve classical Gauss sums (resp. Kloosterman sums).
Hu, Su, Li, Yan, Su Hu, Yan Li
core +1 more source
Quadratic Gauss sums on matrices [PDF]
, 2004 Gauss sums over a finite field are generalized to ones over a matrix ring, related to numbers of solutions of diagonal matrix equations. A similar relation of quadratic Gauss sums of two types is obtained.
Kuroda, Mitsuru, Mitsuru Kuroda
core +1 more source
Open Mathematics, 2018 The main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some ...
Shen Shimeng
doaj +1 more source