Results 31 to 40 of about 3,574 (134)
On Bilinear Exponential and Character Sums with Reciprocals of Polynomials
, 2015 We give nontrivial bounds for the bilinear sums $$ \sum_{u = 1}^{U} \sum_{v=1}^V \alpha_u \beta_v \mathbf{\,e}_p(u/f(v)) $$ where $\mathbf{\,e}_p(z)$ is a nontrivial additive character of the prime finite field ${\mathbb F}_p$ of $p$ elements, with ...
Shparlinski, Igor E.
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Note on the Kloosterman Sum [PDF]
Proceedings of the American Mathematical Society, 1971 The Kloosterman sum \[ ∑ x = 0 ; ( x , p ) = 1 p α − 1 exp
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Kloosterman sums for Chevalley groups [PDF]
Transactions of the American Mathematical Society, 1993 A generalization of Kloosterman sums to a simply connected Chevalley group G G is discussed. These sums are parameterized by pairs ( w , t ) (w,t) where w w is an element of the Weyl group of G G and t t is an element of a
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Airy Sums, Kloosterman Sums, and Salié Sums
Journal of Number Theory, 1997 In 1993 \textit{W. Duke} and \textit{H. Iwaniec} proved that a certain class of cubic exponential sums can be expressed through Kloosterman sums twisted by a cubic character [Contemp. Math. 143, 255-258 (1993; Zbl 0792.11029)]. Their proof made use of one of the Davenport-Hasse theorems.
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Journal of Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Yi-Hsuan, Tu, Fang-Ting
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Large sieve inequalities for exceptional Maass forms and the greatest prime factor of $n^2+1$
Forum of Mathematics, PiWe prove new large sieve inequalities for the Fourier coefficients $\rho _{j\mathfrak {a}}(n)$ of exceptional Maass forms of a given level, weighted by sequences $(a_n)$ with sparse Fourier transforms – including two key types of sequences ...
Alexandru Pascadi
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Visual properties of generalized Kloosterman sums [PDF]
, 2016 For a positive integer m and a subgroup A of the unit group (Z/mZ)x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = ΣuEA e(au+bu-1/m).
Burkhardt, Paula, \u2716 +5 more
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Algebra & Number Theory57 pages, some minor changes done and new references ...
Erdélyi, Márton, Tóth, Árpád
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OPPOSITE‐SIGN KLOOSTERMAN SUM ZETA FUNCTION [PDF]
Mathematika, 2016 We study the meromorphic continuation and the spectral expansion of the oppposite sign Kloosterman sum zeta function, $$(2 \sqrt{mn})^{2s-1}\sum_{\ell=1}^\infty \frac{S(m,-n,\ell)}{\ell^{2s}}$$ for $m,n$ positive integers, to all $s \in \mathbb{C}$. There are poles of the function corresponding to zeros of the Riemann zeta function and the spectral ...
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On Sums of SL(3,Z) Kloosterman Sums
, 2012 We show that sums of the SL(3,Z) long element Kloosterman sum against a smooth weight function have cancellation due to the variation in argument of the Kloosterman sums, when each modulus is at least the square root of the other.
Buttcane, Jack
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