Results 111 to 120 of about 146 (139)

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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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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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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Short Kloosterman Sums with Primes

Mathematical Notes, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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On a generalization of Kloosterman sums

Mathematical Notes, 2015
For integers \(u, v, w\) and natural numbers \(q\), \(d\) with \(d\mid q\). We define \[ K_{q,d}\left(u, v; w\right)=\mathop{\mathop{\sum_{z=1}^{q}}_{(z,q)=1}}_{z\equiv w \;(\bmod d)} e\left(\frac{uz+vz^{-1}}{q}\right), \] where \(e(x)=\text{e}^{2\pi ix}\).
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Modular hyperbolas and bilinear forms of Kloosterman sums

Journal of Number Theory, 2021
I D Shkredov
exaly  

AN ESTIMATION OF KLOOSTERMAN SUMS

Mathematics of the USSR-Izvestiya, 1971
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