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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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Let m, n, q denote positive integers, p a prime, and a, b, h, r, s, t, u, v integers.
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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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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, 1996This 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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On Kloosterman Sums with Oscillating Coefficients
Canadian Mathematical Bulletin, 1999AbstractIn 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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Reducing character sums to Kloosterman sums
Mathematical Notes, 2010In 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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CONGRUENCES FOR SUMS OF POWERS OF KLOOSTERMAN SUMS
International Journal of Number Theory, 2007The nth power-moments Snof classical Kloosterman sums (mod p) are known explicitly only for n ≤ 6. In 2002, we conjectured formulas for Sn(mod 4) for each n > 1, valid for all primes p > n. Here we prove these formulas, and give conjectural congruences for Snmodulo some higher powers of 2 for a few small values of n.
H. TIMOTHY CHOI, RONALD EVANS
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Short Kloosterman Sums with Primes
Mathematical Notes, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A note on the moments of Kloosterman sums
Applicable Algebra in Engineering, Communication and Computing, 2009This 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, 2015For 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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