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Journal of Mathematical Sciences, 2005
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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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Izvestiya: Mathematics, 1995
Kloosterman sums are of the type \[ S(a,b;m)=\sum _{1\leq n\leq m, (m,n)=1} e((an^*+bn)/m), \] where \(nn^*\equiv 1\pmod{m}\). The author restricts the sum here to integers \(n=xy\) with \((xy,m)=1\) and \(x\), \(y\) lying in certain intervals. A complicated but perfectly explicit bound is given for such a modified sum. The bilinear shape of the sum is
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Kloosterman sums are of the type \[ S(a,b;m)=\sum _{1\leq n\leq m, (m,n)=1} e((an^*+bn)/m), \] where \(nn^*\equiv 1\pmod{m}\). The author restricts the sum here to integers \(n=xy\) with \((xy,m)=1\) and \(x\), \(y\) lying in certain intervals. A complicated but perfectly explicit bound is given for such a modified sum. The bilinear shape of the sum is
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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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Mathematical Notes, 1999
The paper investigates Kloosterman double sums with weights of type \[ W(a,b)=\sum_{\substack{ X < x \leq X_1\\ (x,m)=1}} \sum_{\substack{ Y < y \leq Y_1\\ (y,m)=1}} \xi(x) \eta(y) \exp \left (\frac{2 \pi i}{m} (a x^* y^* + b x y) \right). \] Here \(\xi(x)\), \(\eta(y)\) are complex-valued functions, \(0 < X < X_1 \leq 2X\), \(0 < Y < Y_1 \leq 2Y\) and
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The paper investigates Kloosterman double sums with weights of type \[ W(a,b)=\sum_{\substack{ X < x \leq X_1\\ (x,m)=1}} \sum_{\substack{ Y < y \leq Y_1\\ (y,m)=1}} \xi(x) \eta(y) \exp \left (\frac{2 \pi i}{m} (a x^* y^* + b x y) \right). \] Here \(\xi(x)\), \(\eta(y)\) are complex-valued functions, \(0 < X < X_1 \leq 2X\), \(0 < Y < Y_1 \leq 2Y\) and
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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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Studia Scientiarum Mathematicarum Hungarica, 2013
We give optimal bounds for Kloosterman sums that arise in the estimation of Fourier coefficients of Siegel modular forms of genus 2.
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We give optimal bounds for Kloosterman sums that arise in the estimation of Fourier coefficients of Siegel modular forms of genus 2.
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Methods of Estimating Short Kloosterman Sums
Doklady Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the General Kloosterman Sums
Journal of Mathematical Sciences, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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