Results 1 to 10 of about 3,556 (119)

Cancellations Amongst Kloosterman Sums [PDF]

Acta Arithmetica, 2016
We obtain several estimates for bilinear form with Kloosterman sums. Such results can be interpreted as a measure of cancellations amongst with parameters from short intervals.
Shparlinski, I. E., Zhang, T. P.
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On the Generalization of Lehmer Problem and High-Dimension Kloosterman Sums [PDF]

The Scientific World Journal, 2014
For any fixed integer k≥2 and integer r with r, p=1, it is clear that there exist k integers 1≤ai≤p-1 i=1, 2, …, k such that a1a2⋯ak≡r mod p. Let N(k,r;p) denote the number of all a1, a2, ⋯ak such that a1a2⋯ak≡r mod p and 2†a1+a2+⋯ + ak.
Guohui Chen, Han Zhang
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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
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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
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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
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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
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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.
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The largest prime factor of $X^3+2$ [PDF]

, 2001
The largest prime factor of $X^3+2$ has been investigated by Hooley, who gave a conditional proof that it is infinitely often at least as large as $X^{1+\delta}$, with a certain positive constant $\delta$.
Heath-Brown, D. R.
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On the High-Power Mean of the Generalized Gauss Sums and Kloosterman Sums

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 ...
Xinyu Liu, Wenpeng Zhang
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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
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