Previous |  Up |  Next

Article

Keywords:
Hardy sums; the Kloosterman sums; hybrid mean value; asymptotic formula; identity
Summary:
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.
References:
[1] Berndt, B. C.: Analytic Eisenstein series, theta-function, and series relations in the spirit of Ramanujan. J. Reine Angew. Math. 303/304 (1978), 332-365. MR 0514690
[2] Carlitz, L.: The reciprocity theorem for Dedekind sums. Pac. J. Math. 3 (1953), 523-527. DOI 10.2140/pjm.1953.3.523 | MR 0056020 | Zbl 0057.03703
[3] Conrey, J. B., Fransen, E., Klein, R., Scott, C.: Mean values of Dedekind sums. J. Number Theory. 56 (1996), 214-226. DOI 10.1006/jnth.1996.0014 | MR 1373548 | Zbl 0851.11028
[4] Jia, Ch.: On the mean value of Dedekind sums. J. Number Theory. 87 (2001), 173-188. DOI 10.1006/jnth.2000.2580 | MR 1824141 | Zbl 0976.11044
[5] Rademacher, H., Grosswald, E.: ``Dedekind sums'' 16, The Carus Mathematical Monographs. The Mathematical Association of America, Washington D.C. (1972). MR 0357299
[6] Sitaramachandrarao, R.: Dedekind and Hardy sums. Acta Arith. 48 (1987), 325-340. MR 0927374 | Zbl 0635.10002
[7] Zhang, W.: A note on the mean square value of the Dedekind sums. Acta Math. Hung. 86 (2000), 275-289. DOI 10.1023/A:1006724724840 | MR 1756252 | Zbl 0963.11049
[8] Zhang, W.: On the mean values of Dedekind sums. J. Théor. Nombres. 8 (1996), 429-442. DOI 10.5802/jtnb.179 | MR 1438480 | Zbl 0871.11033
[9] Zhang, W., Yi, Y.: On the $2m$-th power mean of certain Hardy sums. Soochow J. Math. 26 (2000), 73-84. MR 1755136 | Zbl 0999.11060
[9] Zhang, W., Yi, Y.: On the $2m$-th power mean of certain Hardy sums. Soochow J. Math. 26 (2000), 73-84. MR 1755136 | Zbl 0999.11060
Partner of
EuDML logo