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Note on the Kloosterman Sum [PDF]

Proceedings of the American Mathematical Society, 1971
The Kloosterman sum \[ ∑ x = 0 ; ( x , p ) = 1 p α − 1 exp
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One special kind of Kloosterman sum and its fourth-power mean

Open Mathematics
This article aims to investigate the calculation problem of the fourth-power mean of the specific Kloosterman sums by utilizing analytic methods and the properties of classical Gauss sums.
Zhang Wenpeng, Wang Li, Liu Xiaoge
doaj   +1 more source

The balanced Voronoi formulas for GL(n)

, 2017
In this paper we show how the GL(N) Voronoi summation formula of [MiSc2] can be rewritten to incorporate hyper-Kloosterman sums of various dimensions on both sides.
Miller, Stephen D., Zhou, Fan
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Visual properties of generalized Kloosterman sums [PDF]

, 2016
For a positive integer m and a subgroup A of the unit group (Z/mZ)x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = ΣuEA e(au+bu-1/m).
Burkhardt, Paula, \u2716, Chan, Alice Zhuo-Yu, \u2714, Currier, Gabriel, \u2716, Garcia, Stephan Ramon, Luca, Florian, Suh, Hong, \u2716   +5 more
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Kloosterman sums for Chevalley groups [PDF]

Transactions of the American Mathematical Society, 1993
A generalization of Kloosterman sums to a simply connected Chevalley group G G is discussed. These sums are parameterized by pairs ( w , t ) (w,t) where w w is an element of the Weyl group of G G and t t is an element of a
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Quantum algorithms for hidden nonlinear structures

, 2007
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm.
Childs, Andrew M., Schulman, Leonard J., Vazirani, Umesh V.   +2 more
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Airy Sums, Kloosterman Sums, and Salié Sums

Journal of Number Theory, 1997
In 1993 \textit{W. Duke} and \textit{H. Iwaniec} proved that a certain class of cubic exponential sums can be expressed through Kloosterman sums twisted by a cubic character [Contemp. Math. 143, 255-258 (1993; Zbl 0792.11029)]. Their proof made use of one of the Davenport-Hasse theorems.
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Twisted Kloosterman sums

Journal of Number Theory, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Yi-Hsuan, Tu, Fang-Ting
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Matrix Kloosterman sums

Algebra & Number Theory
57 pages, some minor changes done and new references ...
Erdélyi, Márton, Tóth, Árpád
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OPPOSITE‐SIGN KLOOSTERMAN SUM ZETA FUNCTION [PDF]

Mathematika, 2016
We study the meromorphic continuation and the spectral expansion of the oppposite sign Kloosterman sum zeta function, $$(2 \sqrt{mn})^{2s-1}\sum_{\ell=1}^\infty \frac{S(m,-n,\ell)}{\ell^{2s}}$$ for $m,n$ positive integers, to all $s \in \mathbb{C}$. There are poles of the function corresponding to zeros of the Riemann zeta function and the spectral ...
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