Displaying similar documents to “The asymptotic distribution of exponential sums. I.”

A hybrid mean value related to certain Hardy sums and Kloosterman sums

Xiaoyan Guo, Wenpeng Zhang (2011)

Czechoslovak Mathematical Journal

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The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.

A hybrid mean value involving two-term exponential sums and polynomial character sums

Han Di (2014)

Czechoslovak Mathematical Journal

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Let q ≥ 3 be a positive integer. For any integers m and n , the two-term exponential sum C ( m , n , k ; q ) is defined by C ( m , n , k ; q ) = ∑ a = 1 q e ( ( m a k + n a ) / q ) , where e ( y ) = e 2 π i y . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.

On the fourth-order linear recurrence formula related to classical Gauss sums

Chen Zhuoyu, Zhang Wenpeng (2017)

Open Mathematics

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Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recurrence formula for it, where τ(ψ) denotes the classical Gauss sums.

Power-moments of SL 3 ( ℤ ) Kloosterman sums

Goran Djanković (2013)

Czechoslovak Mathematical Journal

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Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL 2 and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL 3 have been considered, in which analogous GL 3 -Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL 3 ( ℤ ) . We give formulas...

An identity involving Dedekind sums and generalized Kloosterman sums

Le Huan, Jingzhe Wang, Tingting Wang (2012)

Czechoslovak Mathematical Journal

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The various properties of classical Dedekind sums S ( h , q ) have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums K ( m , n , r ; q ) . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of...