The asymptotic distribution of exponential sums. I.

Patterson, S.J.

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The asymptotic distribution of exponential sums. II.

Patterson, S.J. (2005)

Experimental Mathematics

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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 $q \geq 3$ be a positive integer. For any integers $m$ and $n$ , the two-term exponential sum $C (m, n, k; q)$ is defined by $C (m, n, k; q) = \sum_{a = 1}^{q} e ((m a^{k} + n a) / q)$ , 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 determination of Gauss sums

John H. Loxton (1976-1977)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

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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...

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