Browse > Article
http://dx.doi.org/10.4134/JKMS.2007.44.1.011

HYBRID MEAN VALUE OF GENERALIZED BERNOULLI NUMBERS, GENERAL KLOOSTERMAN SUMS AND GAUSS SUMS  

Liu, Huaning (Department of Mathematics Northwest University)
Zhang, Wenpeng (Department of Mathematics Northwest University)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.1, 2007 , pp. 11-24 More about this Journal
Abstract
The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan's sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.
Keywords
Bernoulli numbers; Kloosterman sums; Gauss sums;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 A. V. Malysev, A generalization of Kloosterman sums and their estimates, Vestnik Leningrad. Univ. 15 (1960), no. 13, 59-75
2 T. M. Apostol, Introduction to analytic number theory, Undergraduate Texts in Math- ematics. Springer-Verlag, New York-Heidelberg, 1976
3 W. Zhang, On the general Kloosterman sums and its fourth power mean, J. Number Theory 104 (2004), no. 1, 156-161   DOI   ScienceOn
4 W. Zhang, On the fourth power mean of the general Kloosterman sums, Indian J. Pure Appl. Math. 35 (2004), no. 2, 237-242
5 H. Liu and W. Zhang, On the hybrid mean value of Gauss sums and generalized Bernoulli numbers, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 6, 113-115   DOI   ScienceOn
6 S. Chowla, On Kloosterman's sum, Norske Vid. Selsk. Forh. (Trondheim) 40 (1967), 70-72
7 T. Estermann, On Kloosterman's sum, Mathematica 8 (1961), 83-86
8 H. W. Leopoldt, Eine Verallgemeinerung der Bernoullischen Zahlen, Abh. Math. Sem. Univ. Hamburg 22 (1958), 131-140   DOI
9 C.-D. Pan and C.-B. Pan, Goldbach's Conjecture, Chuncui Shuxue yu Yingyong Shuxue Zhuanzhu [Series of Monographs in Pure and Applied Mathematics], 7. Kexue Chuban- she (Science Press), Beijing, 1981
10 Y. Yi and W. Zhang, On the 2k-th power mean of inversion of L-functions with the weight of Gauss sums, Acta Math. Sin. (Engl. Ser.) 20 (2004), no. 1, 175-180   DOI
11 W. Zhang, Y. Yi, and X. He, On the 2k-th power mean of Dirichlet L-functions with the weight of general Kloosterman sums, J. Number Theory 84 (2000), no. 2, 199-213   DOI   ScienceOn
12 W. Zhang, The first power mean of the inversion of L-functions and general Klooster- man sums, Monatsh. Math. 136 (2002), no. 3, 259-267   DOI
13 W. Zhang, On a Cochrane sum and its hybrid mean value formula, J. Math. Anal. Appl. 267 (2002), no. 1, 89-96   DOI   ScienceOn
14 W. Zhang and H. Liu, A note on the Cochrane sum and its hybrid mean value formula, J. Math. Anal. Appl. 288 (2003), no. 2, 646-659   DOI   ScienceOn