Construction of Equientangled Bases in Arbitrary Dimensions via Quadratic Gauss Sums and Graph States [PDF]
, 2010 Recently [Karimipour and Memarzadeh, Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space each of dimension $D$ with the following properties: (i) The family continuously interpolates between ...
Gheorghiu, Vlad, Looi, Shiang Yong
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An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group [PDF]
, 2009 The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2).
Maurice R Kibler +1 more
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SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms [PDF]
Symmetry, 2010 We propose a group-theoretical approach to the generalized oscillator algebra Ak recently investigated in J. Phys. A: Math. Theor. 43 (2010) 115303. The case k > or 0 corresponds to the noncompact group SU(1,1) (as for the harmonic oscillator and the ...
Albouy +14 more
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The hybrid power mean of the generalized Gauss sums and the generalized two-term exponential sums
AIMS MathematicsThis article applied the properties of character sums, quadratic character, and classical Gauss sums to study the calculations of the hybrid power mean of the generalized Gauss sums and the generalized two-term exponential sums.
Xue Han, Tingting Wang
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A certain new Gauss sum and its fourth power mean
AIMS Mathematics, 2020 The main purpose of this paper is using the elementary methods and the properties of the Legendre symbol to study the computational problem of the fourth power mean of a certain generalized quadratic Gauss sum, and give two exact calculating formulae for
Yan Zhao, Wenpeng Zhang, Xingxing Lv
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A hybrid mean value of the inversion of L-functions and general quadratic Gauss sums [PDF]
Nagoya Mathematical Journal, 2002 AbstractThe main purpose of this paper is, using the estimates for character sums and the analytic method, to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums, and give two interesting asymptotic formulas.
Zhang, Wenpeng, Deng, Yuping
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On Tractable Exponential Sums [PDF]
, 2010 We consider the problem of evaluating certain exponential sums. These sums take the form $\sum_{x_1,...,x_n \in Z_N} e^{f(x_1,...,x_n) {2 \pi i / N}} $, where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate polynomial with ...
A. Bulatov +10 more
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Double-Janus linear sigma models and generalized reciprocity for Gauss sums [PDF]
Journal of High Energy Physics, 2019 We study the supersymmetric partition function of a 2d linear σ-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other.
O. Ganor +2 more
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Artin's primitive root conjecture -a survey - [PDF]
, 2012 This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background.
Moree, Pieter
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On quadratic Gauss sums and variations thereof [PDF]
, 2014 A number of new terminating series involving and are presented and connected to Gauss quadratic sums. Several new closed forms of generic Gauss quadratic sums are obtained and previously known results are generalized.
M. Glasser, M. Milgram
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