Results 21 to 30 of about 25,118 (105)
On the quadratic residues and their distribution properties
Open Mathematics, 2023 The main purpose of this article is to use elementary methods and properties of classical Gauss sums to determine identities for the number of residue systems of aa mod pp such that aa, a+a¯a+\bar{a}, and a−a¯a-\bar{a} are all quadratic residues ...
Liu Xiaoge, Meng Yuanyuan
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On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers [PDF]
, 2007 We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes.
A. Barg +29 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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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
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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
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Experimental violation of a Bell-like inequality with optical vortex beams [PDF]
, 2015 Optical beams with topological singularities have a Schmidt decomposition. Hence, they display features typically associated with bipartite quantum systems; in particular, these classical beams can exhibit entanglement. This classical entanglement can be
Agarwal, G. S. +5 more
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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
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Levy-Student Distributions for Halos in Accelerator Beams [PDF]
, 2005 We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes.
B. V. Gnedenko +25 more
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A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums
The Scientific World Journal, 2014 The main purpose of this paper is using the analytic method, A. Weil’s classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the ...
Jianghua Li, Tingting Wang
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The value distribution of incomplete Gauss sums
, 2012 It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges.
Chinen +4 more
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