| Title:
|
A hybrid mean value of the Dedekind sums (English) |
| Author:
|
Yang, Hai |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
1055-1063 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Dedekind sums |
| Keyword:
|
Dirichlet $L$-function |
| Keyword:
|
mean value |
| MSC:
|
11F20 |
| MSC:
|
11L40 |
| MSC:
|
11M20 |
| idZBL:
|
Zbl 1224.11085 |
| idMR:
|
MR2738967 |
| . |
| Date available:
|
2010-11-20T13:58:33Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140804 |
| . |
| Reference:
|
[1] Carlitz, L.: The reciprocity theorem of Dedekind sums.Pac. J. Math. 3 (1953), 513-522. MR 0056020, 10.2140/pjm.1953.3.513 |
| Reference:
|
[2] Rademacher, H.: On the transformation of $\log\eta(\tau)$.J. Indian Math. Soc. 19 (1955), 25-30. Zbl 0064.32703, MR 0070660 |
| Reference:
|
[3] Mordell, L. J.: The reciprocity formula for Dedekind sums.Am. J. Math. 73 (1951), 593-598. Zbl 0042.27401, MR 0042449, 10.2307/2372310 |
| Reference:
|
[4] Conrey, J. B., Fransen, E., Klein, R., Scott, C.: Mean values of Dedekind sums.J. Number Theory 56 (1996), 214-226. Zbl 0851.11028, MR 1373548, 10.1006/jnth.1996.0014 |
| Reference:
|
[5] Walum, H.: An exact formula for an average of $L$-series.Il. J. Math. 26 (1982), 1-3. Zbl 0464.10030, MR 0638548 |
| Reference:
|
[6] Zhang, W.: On the mean values of Dedekind sums.J. Théor. Nombres Bordx. 8 (1996), 429-442. Zbl 0871.11033, MR 1438480, 10.5802/jtnb.179 |
| Reference:
|
[7] Toyoizumi, M.: On certain character sums.Acta Arith. 55 (1990), 229-232. Zbl 0702.11054, MR 1067970, 10.4064/aa-55-3-229-232 |
| . |
