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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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Polynomials for Kloosterman Sums
Canadian Mathematical Bulletin, 2007AbstractFix an integer m > 1, and set ζm = exp(2πi/m). Let denote the multiplicative inverse of x modulo m. The Kloosterman sums , satisfy the polynomialwhere the sum and product are taken over a complete system of reduced residues modulo m. Here we give a natural factorization of fm(x), namely,where σ runs through the square classes of the group ...
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Cryptography and Communications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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