Results 31 to 40 of about 40,388 (276)
Note on the quadratic Gauss sums
International Journal of Mathematics and Mathematical Sciences, 2001 Let p be an odd prime and {χ(m)=(m/p)}, m=0,1,...,p−1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ modp which are defined in terms of the Legendre symbol (m/p), (m,p)=1. We study the relation between the Gauss and
George Danas
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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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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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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
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Mutually unbiased phase states, phase uncertainties, and Gauss sums [PDF]
, 2005 Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/sqrt{d), with d the dimension of the finite Hilbert space, are becoming more and more studied for ...
Planat, M., Rosu, H. C.
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Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case
, 2010 Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let $\k$ be a primitive multiplicative character of order $N$ over finite field $\fq$.
B. C. Berndt +18 more
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Finite Fields and Their Applications, 1998 Let \(m\) be an odd positive integer, \(n\) an arbitrary positive integer, and \(p\) a prime which does not divide \(m\). Let \(\mathbb{F}_{p}\) be a prime finite field, \(\mathbb{F}_{q}\) a finite extension of \(\mathbb{F}_{p}\) of degree \(f\), so \(q=p^{f}\), and \( \chi\) a multiplicative character of \(\mathbb{F}_{q}\) of order \(m\). If \( \zeta_{
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On the Hybrid Power Mean of Two-Term Exponential Sums and Cubic Gauss Sums
Journal of Mathematics, 2021 In this paper, an interesting third-order linear recurrence formula is presented by using elementary and analytic methods. This formula is concerned with the calculating problem of the hybrid power mean of a certain two-term exponential sums and the ...
Shaofan Cao, Tingting Wang
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Tokyo Journal of Mathematics, 2012 Let \(p > 2\) be a prime number, \(\mathbb F_p\) the prime finite field with \(p\) elements, \(\mathbb F^*_p\) its multiplicative cyclic group of order \(p-1\) and \(i = \sqrt{-1}\). The classical Gauss sum \(g_p\) is given by \[ \tau_p= \sum_{x \in \mathbb F^*_p} \left( \frac{x}{p} \right) e^{2 { \pi}i x/p}, \] where \( \left( \frac{x}{p} \right)\) is
GOMI, Yasushi +2 more
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A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums
Journal of Applied Mathematics, 2014 The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula
Liu Miaohua, Li Xiaoxue
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