On the mean value of general Cochrane sum

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On the mean value of general Cochrane sum

Dongmei Ren and Yuan Yi

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 1 (2010), 1-5.

Abstract

In this paper, the general Cochrane sum is defined. The main purpose is to study the mean square value problem of general Cochrane sum by using the estimates for trigonometric sums and the properties of general Kloosterman sum, and finally give a sharp asymptotic formula.

Primary Subjects: 11F20, 11L03, 11L05

Keywords: Cochrane sum; Legendre's symbol; Kloosterman sum; Gauss sum

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1262271515
Digital Object Identifier: doi:10.3792/pjaa.86.1
Zentralblatt MATH identifier: 05690865
Mathematical Reviews number (MathSciNet): MR2598816

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References

S. Chowla, On Kloosterman's sum, Norske Vid. Selsk. Forh. (Trondheim) 40 (1967), 70--72.

Mathematical Reviews (MathSciNet): MR228452

A. V. Malyšev, A generalization of Kloosterman sums and their estimates, Vestnik Leningrad. Univ. 15 (1960), no. 13, 59--75.

Mathematical Reviews (MathSciNet): MR125084

C. Pan and C. Pan, Goldbach Conjecture, Science Press, Beijing, 1981.

W. Zhang and Y. Yi, On the upper bound estimate of Cochrane sums, Soochow J. Math. 28 (2002), no. 3, 297--304.

Mathematical Reviews (MathSciNet): MR1926326

Zentralblatt MATH: 1016.11038

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