Previous |  Up |  Next

Article

Keywords:
Dedekind sums; Dirichlet $L$-function; mean value
Summary:
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
References:
[1] Carlitz, L.: The reciprocity theorem of Dedekind sums. Pac. J. Math. 3 (1953), 513-522. DOI 10.2140/pjm.1953.3.513 | MR 0056020
[2] Rademacher, H.: On the transformation of $\log\eta(\tau)$. J. Indian Math. Soc. 19 (1955), 25-30. MR 0070660 | Zbl 0064.32703
[3] Mordell, L. J.: The reciprocity formula for Dedekind sums. Am. J. Math. 73 (1951), 593-598. DOI 10.2307/2372310 | MR 0042449 | Zbl 0042.27401
[4] 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
[5] Walum, H.: An exact formula for an average of $L$-series. Il. J. Math. 26 (1982), 1-3. MR 0638548 | Zbl 0464.10030
[6] Zhang, W.: On the mean values of Dedekind sums. J. Théor. Nombres Bordx. 8 (1996), 429-442. DOI 10.5802/jtnb.179 | MR 1438480 | Zbl 0871.11033
[7] Toyoizumi, M.: On certain character sums. Acta Arith. 55 (1990), 229-232. DOI 10.4064/aa-55-3-229-232 | MR 1067970 | Zbl 0702.11054
Partner of
EuDML logo