Results 11 to 20 of about 859,926 (192)
Kloosterman sum identities and low-weight codewords in a cyclic code with two zeros
Finite Fields Their Appl., 2006 We apply relations of n-dimensional Kloosterman sums to exponential sums over finite fields to count the number of low-weight codewords in a cyclic code with two zeros.
Marko Moisio +3 more
core +2 more sources
A transform property of Kloosterman sums
Discrete Applied Mathematics, 2010 Kloosterman sums \(K_k(a,b)\) are of interest in many parts of mathematics. They are defined as \(K_k(a,b)=\sum_{\gamma \in {\mathbb{F}_{q^k}^\ast}}\chi(\text{trace}(a\gamma+b\gamma^{-1})\), where \(\chi\) in an additive character of the finite field \({\mathbb F}_{q}\). Here \(q\) is a prime power and the trace is relative to \({\mathbb F}_q\).
Ian F. Blake, Theodoulos Garefalakis
openaire +2 more sources
On the moments of Kloosterman sums and fibre products of Kloosterman curves
Finite Fields and Their Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Moisio, Marko
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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
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
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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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On Certain Values of Kloosterman Sums [PDF]
IEEE Transactions on Information Theory, 2009 Let $K_{q^n}(a)$ be a Kloosterman sum over the finite field $\F_{q^n}$ of characteristic $p$. In this note so called subfield conjecture is proved in case $p>3$: if $a\ne0$ belongs to the proper subfield $\F_q$ of $\F_{q^n}$, then $K_{q^n}(a)\ne-1$. This completes recent works on the subfield conjecture by Shparlinski, and Moisio and Lisonek.
Väänänen Keijo +2 more
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An efficient deterministic test for Kloosterman sum zeros [PDF]
, 2013 We propose a simple deterministic test for deciding whether or not an element a ∈ F×2n or F×3n is a zero of the corresponding Kloosterman sum over these fields, and rigorously analyse its runtime. The test seems to have been overlooked in the literature.
Granger, Robert, Ahmadi, Omran
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On Some Identities Involving Certain Hardy Sums and a Kloosterman Sum
Ukrainian Mathematical Journal, 2020 We propose a new reciprocity theorem for the Hardy sum s5(h, p). In addition, a hybrid mean-value problem involving the Hardy sum s4(h, p) and a Kloosterman sum is studied and two exact computational formulas are obtained.
M. C. Dağlı
semanticscholar +1 more source
Opposite Sign Kloosterman Sum Zeta Function [PDF]
, 2015 We study the meromorphic continuation and the spectral expansion of the oppposite sign Kloosterman sum zeta function, $$(2\pi \sqrt{mn})^{2s-1}\sum_{\ell=1}^\infty \frac{S(m,-n,\ell)}{\ell^{2s}}$$ for $m,n$ positive integers, to all $s \in \mathbb{C ...
E. M. Kıral
semanticscholar +1 more source