Results 1 to 10 of about 7,901 (118)

On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums

Journal of Mathematics, 2021
The main purpose of this paper is to use the elementary and analytic methods, the properties of Gauss sums, and character sums to study the computational problem of a certain hybrid power mean involving the Dedekind sums and a character sum analogous to ...
Xiaoling Xu
doaj   +1 more source

A Note on Cube-Full Numbers in Arithmetic Progression

Journal of Mathematics, 2021
We obtain an asymptotic formula for the cube-full numbers in an arithmetic progression n≡lmod q, where q,l=1. By extending the construction derived from Dirichlet’s hyperbola method and relying on Kloosterman-type exponential sum method, we improve the ...
Mingxuan Zhong, Yuankui Ma
doaj   +1 more source

Generalization of the Lehmer problem over incomplete intervals

Journal of Inequalities and Applications, 2023
Let α ≥ 2 $\alpha \geq 2$ , m ≥ 2 $m\geq 2 $ be integers, p be an odd prime with p ∤ m ( m + 1 ) $p\nmid m (m+1 )$ , 0 < λ 1 $0 max { [ 1 λ 1 ] , [ 1 λ 2 ] } $q=p^{\alpha }> \max \{ [ \frac{1}{\lambda _{1}} ], [ \frac{1}{\lambda _{2}} ] \}$ .
Zhaoying Liu, Di Han
doaj   +1 more source

Cancellations amongst Kloosterman sums [PDF]

Acta Arithmetica, 2016
10 ...
Shparlinski, Igor E., Zhang, Tianping
openaire   +2 more sources

Some Identities Involving Certain Hardy Sums and General Kloosterman Sums

Mathematics, 2020
Using the properties of Gauss sums, the orthogonality relation of character sum and the mean value of Dirichlet L-function, we obtain some exact computational formulas for the hybrid mean value involving general Kloosterman sums K ( r , l , λ ...
Huifang Zhang, Tianping Zhang
doaj   +1 more source

Sign changes of Kloosterman sums with almost prime moduli [PDF]

, 2014
We prove that the Kloosterman sum $S(1,1;c)$ can change sign infinitely often as $c$ runs over squarefree moduli with at most 10 prime factors, which improves the previous results of E. Fouvry and Ph. Michel, J. Sivak-Fischler and K.
Xi, Ping
core   +1 more source

Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and norm [PDF]

, 2007
Let $\F_q$ ($q=p^r$) be a finite field. In this paper the number of irreducible polynomials of degree $m$ in $\F_q[x]$ with prescribed trace and norm coefficients is calculated in certain special cases and a general bound for that number is obtained ...
Moisio, Marko
core   +1 more source

Upper bound estimate of incomplete Cochrane sum

Open Mathematics, 2017
By using the properties of Kloosterman sum and Dirichlet character, an optimal upper bound estimate of incomplete Cochrane sum is given.
Ma Yuankui, Peng Wen, Zhang Tianping
doaj   +1 more source

An Algorithm for the explicit evaluation of GL(n, R) Kolsterman sums [PDF]

, 2009
An algorithm for the explicit evaluation of Kloosterman sums for GL(n, R) for n ≥2 and an implementation in the Mathematics package GL(n) pack are ...
Broughan, Kevin A.
core   +2 more sources

Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method [PDF]

, 2016
We prove a bound for quintilinear sums of Kloosterman sums, with congruence conditions on the "smooth" summation variables. This generalizes classical work of Deshouillers and Iwaniec, and is key to obtaining power-saving error terms in applications ...
Drappeau, Sary
core   +2 more sources