Results 1 to 10 of about 146 (124)

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 ...
Wenpeng Zhang
exaly   +5 more sources

A Hybrid Mean Value Involving Dedekind Sums and the Generalized Kloosterman Sums

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
doaj   +4 more sources

Visual properties of generalized Kloosterman sums

Journal of Number Theory, 2016
For a positive integer $m$ and a subgroup $Λ$ of the unit group $(\mathbb{Z}/m\mathbb{Z})^\times$, the corresponding generalized Kloosterman sum is the function $K(a,b,m,Λ) = \sum_{u \in Λ}e(\frac{au + bu^{-1}}{m})$. Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when
Stephan Ramon Garcia, Florian Luca
exaly   +6 more sources

The equidistribution of elliptic Dedekind sums and generalized Selberg–Kloosterman sums

Research in Number Theory
14 ...
Tian An Wong
exaly   +4 more sources

On a Kind of Dirichlet Character Sums [PDF]

Abstract and Applied Analysis, 2013
Let p≥3 be a prime and let χ denote the Dirichlet character modulo p.
Rong Ma, Yulong Zhang, Guohe Zhang
doaj   +2 more sources

Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums [PDF]

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020
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 $M\geq q^{3/8+δ}$ for any $δ>0$. This range, which matches Burgess's range, is identical with the best results previously known only for simpler exponentials of monomials ...
Kowalski, Emmanuel, Michel, Philippe, Sawin, Will   +2 more
openaire   +4 more sources

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.
Yangbo Ye
openaire   +4 more sources

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
exaly   +2 more sources

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
L. Alayne Parson
openaire   +2 more sources

The Weil bound for generalized Kloosterman sums of half-integral weight

Forum Mathematicum
Abstract Let L be an even lattice of odd rank with discriminant group L ′ /
Nickolas Andersen, Amy Woodall
exaly   +4 more sources