Results 21 to 30 of about 884,151 (313)
Some identities involving Gauss sums
AIMS Mathematics, 2022 We calculate several identities involving some Gauss sums of the $ 2^k $-order character modulo an odd prime $ p $ by using the elementary and analytic methods, and finally give several exact and interesting formulae for them.
Xi Liu
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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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Hypergeometric decomposition of symmetric K3 quartic pencils [PDF]
, 2020 We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this ...
Doran, Charles F. +5 more
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Factorizing Numbers with the Gauss Sum Technique: NMR Implementations [PDF]
, 2007 Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors.
Dieter Suter +8 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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A Hybrid Mean Value Involving Dedekind Sums and the Generalized Kloosterman Sums
Journal of Mathematics, 2021 In this paper, we use the mean value theorem of Dirichlet L-functions and the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the general Kloosterman sums and give an interesting identity for ...
Xiaowei Pan, Xiaoyan Guo
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Classical Simulation of Quantum Circuits by Half Gauss Sums [PDF]
Communications in Mathematical Physics, 2018 We give an efficient algorithm to evaluate a certain class of exponential sums, namely the periodic, quadratic, multivariate half Gauss sums. We show that these exponential sums become #P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage ...
Kaifeng Bu, Dax Enshan Koh
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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
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On the character sums analogous to high dimensional Kloosterman sums
AIMS Mathematics, 2022 The main purpose of this paper is using the properties of the classical Gauss sums and the analytic methods to study the computational problem of one kind of character sums analogous to high dimensional Kloosterman sums, and give some interesting ...
Jianghua Li , Xi Zhang
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New Identities Dealing with Gauss Sums
Symmetry, 2020 In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the ...
Wenpeng Zhang, Abdul Samad, Zhuoyu Chen
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