Results 11 to 20 of about 185 (158)
A note on the mean value of the general Kloosterman sums [PDF]
Czechoslovak Mathematical Journal, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yao, Weili, Liu, Huaning
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On the general Kloosterman sum and its fourth power mean
Journal of Number Theory, 2004 Let \(q \geq 3\) be a positive integer and let \(\chi\) denote a Dirichlet character mod \(q\). For any integers \(m\) and \(n\), the general Kloosterman sum \(S(m ,n , \chi ; q)\) is defined as follows: \[ S(m,n, \chi ; q) = \mathop{{\sum}^*}_{a=1}^q \chi(a) e\left(\frac {ma+n \overline{a}}{q} \right), \] where \(e(y) = e^{2 \pi i y}\) and \(\sum ...
Wenpeng, Zhang
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On the fourth power mean of the general k th Kloosterman sums [PDF]
Advances in Difference Equations, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Xiaoyan, Geng, Guohua, Pan, Xiaowei
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General Kloosterman sums over the ring of Gaussian integers [PDF]
Ukrainian Mathematical Journal, 2007 The general Kloosterman sum K(m, n; k; q) over ℤ was studied by S. Kanemitsu, Y. Tanigawa, Yuan Yi, and Wenpeng Zhang in their research of the problem of D. H. Lehmer. In the present paper, we obtain similar estimates for K(α, β; k; γ) over ℤ[i]. We also consider the sum \(\tilde K(\alpha ,\beta ;h,q;k)\), which does not have an analog in the ring ℤ ...
S. P. Varbanets
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INVERSION OF L-FUNCTIONS, GENERAL KLOOSTERMAN SUMS WEIGHTED BY INCOMPLETE CHARACTER SUMS [PDF]
Journal of the Korean Mathematical Society, 2010 The main purpose of this paper is using estimates for char- acter sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirich- let L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.
Xiaobeng Zhang, Huaning Liu
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Newton polygons for L-functions of generalized Kloosterman sums [PDF]
Forum Mathematicum, 2021 Abstract 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. In order to determine the Hodge polygon, we explicitly construct a basis of the top-dimensional Dwork cohomology.
Wang, Chunlin, Yang, Liping
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An identity involving Dedekind sums and generalized Kloosterman sums [PDF]
Czechoslovak Mathematical Journal, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huan, Le, Wang, Jingzhe, Wang, Tingting
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Ukrainian Mathematical Journal, 2023 UDC 511 We study a hybrid mean-value problem related to the generalized Dedekind sum, certain generalized Hardy sums, and Kloosterman sum and obtain several meaningful conclusions by means of the analytic method and the properties of the character sum and the Gauss sum.
Dağlı, Muhammet Cihat, Sever, Hamit
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Symplectic Kloosterman Sums and Poincar\'e Series
, 2023 We prove power-saving bounds for general Kloosterman sums on $\operatorname{Sp}(4)$ associated to all Weyl elements via a stratification argument coupled with $p$-adic stationary phase methods. We relate these Kloosterman sums to the Fourier coefficients
Man, Siu Hang
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Second moments of Dirichlet $L$-functions weighted by Kloosterman sums [PDF]
, 2012 summary:For the general modulo $q\geq 3$ and a general multiplicative character $\chi $ modulo $q$, the upper bound estimate of $ |S(m, n, 1, \chi , q)| $ is a very complex and difficult problem. In most cases, the Weil type bound for $ |S(m, n, 1, \chi ,
Wang, Tingting
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