On the High-Power Mean of the Generalized Gauss Sums and Kloosterman Sums [PDF]
Mathematics, 2019 The main aim of this paper is to use the properties of the trigonometric sums and character sums, and the number of the solutions of several symmetry congruence equations to research the computational problem of a certain sixth power mean of the generalized Gauss sums and generalized Kloosterman sums, and to give two exact computational formulae for ...
Wenpeng Zhang
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HYBRID MEAN VALUE OF GENERALIZED BERNOULLI NUMBERS, GENERAL KLOOSTERMAN SUMS AND GAUSS SUMS [PDF]
Journal of the Korean Mathematical Society, 2007 The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan’s sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.
Huaning Liu, Wenpeng Zhang
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On the conductor of cohomological transforms [PDF]
, 2020 In the analytic study of trace functions of $\ell$-adic sheaves over finite fields, a crucial issue is to control the conductor of sheaves constructed in various ways. We consider cohomological transforms on the affine line over a finite field which have
Fouvry, Étienne +2 more
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Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits [PDF]
, 2020 One of the lowest-order corrections to Gaussian quantum mechanics in infinite-dimensional Hilbert spaces are Airy functions: a uniformization of the stationary phase method applied in the path integral perspective.
Kocia, Lucas, Love, Peter
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Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method [PDF]
, 2016 We prove a bound for quintilinear sums of Kloosterman sums, with congruence conditions on the "smooth" summation variables. This generalizes classical work of Deshouillers and Iwaniec, and is key to obtaining power-saving error terms in applications ...
Drappeau, Sary
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Inequalities for differences of Dyson's rank for all odd moduli [PDF]
, 2010 Kathrin Bringmann (Mathematisches Institut, Universität Köln, Weyertal 86-90, D-50931 Köln, Germany) Ben Kane (Wiskunde Afdeling, Radboud Universiteit, Postbus 9010, 6500 GL, Nijmegen, Netherlands ...
Bringmann, K, Kane, B
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Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams [PDF]
, 2017 We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in ...
Ablinger, J. +7 more
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ON FOURIER COEFFICIENTS OF SIEGEL MODULAR FORMS OF DEGREE TWO WITH RESPECT TO CONGRUENCE SUBGROUPS [PDF]
, 2011 We prove a formula of Petersson’s type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficient.
CHIDA, MASATAKA +2 more
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On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields
, 2010 Let $\cC$ be a smooth absolutely irreducible curve of genus $g \ge 1$ defined over $\F_q$, the finite field of $q$ elements. Let $# \cC(\F_{q^n})$ be the number of $\F_{q^n}$-rational points on $\cC$. Under a certain multiplicative independence condition
Ahmadi, Omran, Shparlinski, Igor E.
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Random matrix theory, the exceptional Lie groups, and L-functions
, 2002 There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions.
Bogomolny E B +29 more
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