Results 1 to 10 of about 108 (105)
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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Visual properties of generalized Kloosterman sums
Journal of Number Theory, 2016 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 ...
Burkhardt, Paula +5 more
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Families of generalized Kloosterman sums
, 2013 36 pages, 4 ...
Haessig, C. Douglas, Sperber, Steven
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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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The generalized Kloosterman's sums and its fourth power mean
AIMS Mathematics, 2023 <abstract><p>The main purpose of this article is to study the calculating problem of one kind fourth power mean of the generalized Kloosterman's sums and provide an accurate calculating formula for it utilizing analytical methods and character sums' properties.
Junfeng Cui, Li Wang
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Kuznetsov Formulas for Generalized Kloosterman Sums
Rocky Mountain Journal of Mathematics, 1997 The Kuznetsov trace formula [\textit{N. V. Kuznetsov}, Mat. Sb., Nov. Ser. 111(153), 334-383 (1980; Zbl 0427.10016)] relates a weighted sum of classical Kloosterman sums to a weighted sum of Fourier coefficients of \(GL(2)\) automorphic forms and other spectral information.
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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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On the Generalization of Lehmer Problem and High-Dimension Kloosterman Sums [PDF]
The Scientific World Journal, 2014 For any fixed integerk≥2and integerrwithr, p=1, it is clear that there existkintegers1≤ai≤p-1 i=1, 2, …, ksuch thata1a2⋯ak≡r mod p. LetN(k,r;p)denote the number of alla1, a2, ⋯aksuch thata1a2⋯ak≡r mod pand 2†a1+a2+⋯ + ak. In this paper, we will use the analytic method and the estimate for high-dimension Kloosterman sums to study the asymptotic ...
Guohui Chen, Han 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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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 (
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