Results 161 to 170 of about 859,926 (192)

On the Values of Kloosterman Sums

IEEE Transactions on Information Theory, 2009
Given a prime p and a positive integer n, we show that the shifted Kloosterman sums SigmaxisinF p nPsi(x + alphaxpn-2)=SigmaxisinF* p nPsi(x+alphax-1)+1, alphaisinF*pn where Psi is a nontrivial additive character of a finite field Fpn of pn elements, do not vanish if alpha belongs to a small subfield Fpm sube Fpn.
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A hybrid mean value involving hyper-Kloosterman sums and mth Cochrane sum

Lithuanian Mathematical Journal
Zhefeng Xu, Xu Zhefeng
exaly   +2 more sources

Kloosterman sums

2020
These are a set of notes that introduces the classical Kloosterman sums and proves their basic properties. Kloosterman's bound is proved for the sums which is weaker than the sharp Weil bound. Bounds due to Esterman are also proved and also Selberg's identity is proved for Kloosterman sums.
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On Kloosterman's sum

Mathematika, 1961
Let m, n, q denote positive integers, p a prime, and a, b, h, r, s, t, u, v integers.
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On the Mean Value of the Generalized Dedekind Sum and Certain Generalized Hardy Sums Weighted by the Kloosterman Sum

Ukrainian Mathematical Journal, 2023
M. C. Dağlı, Hamit Sever
semanticscholar   +1 more source

Kloosterman Sums and their Applications: A Review

Results in Mathematics, 1996
This paper lists results, and explains some concepts and results, in the areas of automorphic forms (holomorphic as well as real analytic ones) for cofinite discrete groups of motions in the upper half plane, Kloosterman sums, Hecke operators, Selberg trace formula, Kuznetsov sum formula, representation of \(SL_2\) over the adeles.
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Reducing character sums to Kloosterman sums

Mathematical Notes, 2010
In this paper the authors apply a bound for very short Kloosterman type sums to deduce a bound for a mean-value of short sums of Dirichlet characters. For details, define \[ S^*=\mathop{{\sum}^*}_{\chi (\bmod \;q )}\chi(n)\overline{\chi}(m) \left(\sum_{u}\alpha_u\chi(u)\right)\left(\sum_{v}\beta_v\chi(v)\right)\left|L_f(\chi)\right|^2, \] where the ...
Friedlander, J. B., Iwaniec, H.
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On Kloosterman Sums with Oscillating Coefficients

Canadian Mathematical Bulletin, 1999
AbstractIn this paper we prove: for any positive integers a and q with (a, q) = 1, we have uniformlyThis improves the previous bound obtained by D. Hajela, A. Pollington and B. Smith [5].
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A note on the moments of Kloosterman sums

Applicable Algebra in Engineering, Communication and Computing, 2009
This paper considers several types of Kloosterman sums and proves identities between such sums. Three main types are considered: Kloosterman sums \(K_n(a)\) of degree \(n\), \(m\)-dimensional Kloosterman sums \(K^{(m)}(a)\), and \(m\)-dimensional Kloosterman sums \(K_n^{(m)}(a)\) of degree \(n\). In order to define these, we recall some notation: \(p\)
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Generalized Kloosterman sum with primes

Proceedings of the Steklov Institute of Mathematics, 2017
M. Korolev
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