Home Mathematics On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
Article
Licensed
Unlicensed Requires Authentication

On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums

  • Ma Rong EMAIL logo and Zhang Wenpeng
Published/Copyright: July 29, 2015
Become an author with De Gruyter Brill

Abstract

The main purpose of this paper is using the analytic methods and the estimation of Dirichlet character of polynomials to study the asymptotic properties of one kind hybrid mean value involving the Dedekind sums and Kloosterman sums, and give two interesting asymptotic formulae.

References

[1] APOSTOL, T. M.: Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.10.1007/978-1-4757-5579-4Search in Google Scholar

[2] BURGESS, D. A.: On Dirichlet characters of polynomials, Proc. Lond. Math. Soc. (3) 13 (1963), 537-548.10.1112/plms/s3-13.1.537Search in Google Scholar

[3] CARLITZ, L.: The reciprocity theorem of Dedekind sums, Pacific J. Math. 3 (1953), 513-522.10.2140/pjm.1953.3.513Search in Google Scholar

[4] CHAOHUA, J.: On the mean value of Dedekind sums, J. Number Theory 87 (2001), 173-188.10.1006/jnth.2000.2580Search in Google Scholar

[5] CHOWLA, S.: On Kloosterman’s sum, Norkse Vid. Selbsk. Fak. Frondheim. 40 (1967), 70-72.Search in Google Scholar

[6] CONREY, J. B.-FRANSEN, E.-KLEIN, R.-SCOTT, C.: Mean values of Dedekind sums, J. Number Theory 56 (1996), 214-226.10.1006/jnth.1996.0014Search in Google Scholar

[7] MALYSHEV, A. V.: A generalization of Kloosterman sums and their estimates, Vestnik Leningrad Univ. (Vestnik St. Petersburg Univ. Math.) 15 (1960), 59-75 (Russian).Search in Google Scholar

[8] RADEMACHER, H.: On the transformation of log η(τ), J. Indian Math. Soc. 19 (1955), 25-30.Search in Google Scholar

[9] RADEMACHER, H.: Dedekind Sums. Carus Math. Monogr., Math. Assoc. America, Washington, DC, 1972.10.5948/UPO9781614440161Search in Google Scholar

[10] WALUM, H.: An exact formula for an average of L-series, Illinois J. Math. 26 (1982), 1-3.10.1215/ijm/1256046895Search in Google Scholar

[11] WENPENG, Z.: A note on the mean square value of the Dedekind sums, Acta Math. Hungar. 86 (2000), 275-289.10.1023/A:1006724724840Search in Google Scholar

[12] WENPENG, Z.: On the mean values of Dedekind sums, J. Th´eor. Nombres Bordeaux 8 (1996), 429-442.10.5802/jtnb.179Search in Google Scholar

[13] WENPENG, Z.: On the fourth power mean of the general Kloosterman sums, Indian J. Pure Appl. Math. 35 (2004), 237-242.Search in Google Scholar

[14] WENPENG, Z.: On the fourth power mean of Dirichlet L-functions. In: Lecture Notes in Contemporary Mathematics 1989, Science Press, Beijing, 1990, pp. 173-179.Search in Google Scholar

[15] HUA, L. K.: Introduction to Number Theory, Springer-Verlag, Berlin-New York, 1982.Search in Google Scholar

Received: 2012-5-17
Accepted: 2012-11-22
Published Online: 2015-7-29
Published in Print: 2015-6-1

© Mathematical Institute Slovak Academy of Sciences

Downloaded on 15.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0034/html
Scroll to top button