A Hybrid Mean Value Involving Dedekind Sums and the Generalized Kloosterman Sums [PDF]
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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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 ...
Xinyu Liu, Wenpeng Zhang
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Newton polygons for L-functions of generalized Kloosterman sums [PDF]
Forum Mathematicum, 2021 In the present paper, we study the Newton polygons for the L-functions of n-variable generalized Kloosterman sums. Generally, the Newton polygon has a topological lower bound, called the Hodge polygon.
Chunlin Wang, Liping Yang
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Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2018 We prove non-trivial bounds for bilinear forms with hyper-Kloosterman sums with characters modulo a prime $q$ which, for both variables of length $M$, are non-trivial as soon as $M\geq q^{3/8+\delta}$ for any $\delta>0$. This range, which matches Burgess'
E. Kowalski, P. Michel, W. Sawin
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The Weil bound for generalized Kloosterman sums of half-integral weight [PDF]
Forum Mathematicum, 2023 Let L be an even lattice of odd rank with discriminant group L ′ / L {L^{\prime}/L} , and let α , β ∈ L ′ / L {\alpha,\beta\in L^{\prime}/L} . We prove the Weil bound for the Kloosterman sums S α , β ( m , n , c ) {S_{\alpha,\beta}(m,n,c)} of half ...
Nickolas Andersen +2 more
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The equidistribution of elliptic Dedekind sums and generalized Selberg–Kloosterman sums [PDF]
Research in Number TheoryWe show that the values of elliptic Dedekind sums, after normalization, are equidistributed mod 1. The key ingredient is a non-trivial bound on generalized Selberg–Kloosterman sums for discrete subgroups of PSL2(C)\documentclass[12pt]{minimal ...
Kim Klinger-Logan, Tian An Wong
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Visual properties of generalized Kloosterman sums [PDF]
Journal of Number Theory, 2015 For a positive integer $m$ and a subgroup $ $ of the unit group $(\mathbb{Z}/m\mathbb{Z})^\times$, the corresponding generalized Kloosterman sum is the function $K(a,b,m, ) = \sum_{u \in }e(\frac{au + bu^{-1}}{m})$. Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features ...
Paul Burkhardt +5 more
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Generalized Kloosterman sums and the Fourier coefficients of cusp forms [PDF]
Transactions of the American Mathematical Society, 1976 Certain generalized Kloosterman sums connected with congruence subgroups of the modular group and suitably restricted multiplier systems of half-integral degree are studied. Then a Fourier coefficient estimate is obtained for cusp forms of half-integral degree on congruence subgroups of the modular group and the Hecke groups G (
L. Parson
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$L$-functions for families of generalized Kloosterman sums and $p$-adic differential equations [PDF]
, 2020 In this paper, we focus on a family of generalized Kloosterman sums over the torus. With a few changes to Haessig and Sperber's construction, we derive some relative $p$-adic cohomologies corresponding to the $L$-functions.
Chunlin Wang, Liping Yang
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HYBRID MEAN VALUE OF THE GENERALIZED KLOOSTERMAN SUMS AND DIRICHLET CHARACTER OF POLYNOMIALS [PDF]
, 2013 Wang Jingzhe
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