Results 21 to 30 of about 3,574 (134)

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
core   +1 more source

Fourier expansions of complex-valued Eisenstein series on finite upper half planes

International Journal of Mathematics and Mathematical Sciences, 2006
We consider complex-valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp).
Anthony Shaheen, Audrey Terras
doaj   +1 more source

Legendre sums, Soto–Andrade sums and Kloosterman sums [PDF]

Pacific Journal of Mathematics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

A Conversion Formula for One Kind Fourth Power Mean of Kloosterman Sums and the Character Sums Module p

Journal of Mathematics
The primary contribution of this paper is to research one kind special Kloosterman sums using analytic method. We translate one kind fourth power mean of the Kloosterman sums into the character sums of one kind polynomials. It is possible to construct an
Shushu Ning, Xuexia Wang
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Exponential sums with automatic sequences

, 2017
We show that automatic sequences are asymptotically orthogonal to periodic exponentials of type $e_q(f(n))$, where $f$ is a rational fraction, in the P\'olya-Vinogradov range.
Drappeau, Sary, Müllner, Clemens
core   +3 more sources

Double sums of Kloosterman sums in finite fields [PDF]

Finite Fields and Their Applications, 2019
We bound double sums of Kloosterman sums over a finite field ${\mathbb F}_{q}$, with one or both parameters ranging over an affine space over its prime subfield ${\mathbb F}_p \subseteq {\mathbb F}_{q} $. These are finite fields analogues of a series of recent results by various authors in finite fields and residue rings.
Macourt, Simon, Shparlinski, Igor E.
openaire   +2 more sources

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

On some kloosterman sums

manuscripta mathematica, 1991
Let \({\mathbb{F}}_ q\) be the finite field with q elements, V be a finite- dimensional vector space over \({\mathbb{F}}_ q\), dim V\(=n\), \(L_ 1\), \(L_ 2\) linear forms and Q a quadratic form on V. The author proves an upper bound for the Kloosterman sum \[ K(L_ 1,L_ 2;Q):=\sum_{Q(v)\neq 0}\chi ((L_ 1(v)+L_ 2(v)(Q(v))^{-1}), \] where \(\chi\) is a ...
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Symplectic Kloosterman sums and Poincaré series [PDF]

The Ramanujan Journal, 2021
AbstractWe prove power-saving bounds for general Kloosterman sums on $${\text {Sp}}(4)$$ Sp ( 4 ) associated to all Weyl elements via a stratification argument coupled with p-adic stationary phase methods.
openaire   +2 more sources

The hybrid power mean involving the Kloosterman sums and Dedekind sums

Open Mathematics
Kloosterman sums and Dedekind sums are two important sums in analytic number theory, the study of their various properties is a very interesting subject.
Li Ruiyang, Chen Long
doaj   +1 more source