| Title:
|
A hybrid mean value related to certain Hardy sums and Kloosterman sums (English) |
| Author:
|
Guo, Xiaoyan |
| Author:
|
Zhang, Wenpeng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
759-769 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Hardy sums |
| Keyword:
|
the Kloosterman sums |
| Keyword:
|
hybrid mean value |
| Keyword:
|
asymptotic formula |
| Keyword:
|
identity |
| MSC:
|
11L05 |
| MSC:
|
11M20 |
| MSC:
|
11N37 |
| idZBL:
|
Zbl 1249.11088 |
| idMR:
|
MR2853089 |
| DOI:
|
10.1007/s10587-011-0024-z |
| . |
| Date available:
|
2011-09-22T14:45:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141636 |
| . |
| Reference:
|
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| Reference:
|
[2] Carlitz, L.: The reciprocity theorem for Dedekind sums.Pac. J. Math. 3 (1953), 523-527. Zbl 0057.03703, MR 0056020, 10.2140/pjm.1953.3.523 |
| Reference:
|
[3] 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:
|
[4] Jia, Ch.: On the mean value of Dedekind sums.J. Number Theory. 87 (2001), 173-188. Zbl 0976.11044, MR 1824141, 10.1006/jnth.2000.2580 |
| Reference:
|
[5] Rademacher, H., Grosswald, E.: ``Dedekind sums'' 16, The Carus Mathematical Monographs.The Mathematical Association of America, Washington D.C. (1972). MR 0357299 |
| Reference:
|
[6] Sitaramachandrarao, R.: Dedekind and Hardy sums.Acta Arith. 48 (1987), 325-340. Zbl 0635.10002, MR 0927374, 10.4064/aa-48-4-325-340 |
| Reference:
|
[7] Zhang, W.: A note on the mean square value of the Dedekind sums.Acta Math. Hung. 86 (2000), 275-289. Zbl 0963.11049, MR 1756252, 10.1023/A:1006724724840 |
| Reference:
|
[8] Zhang, W.: On the mean values of Dedekind sums.J. Théor. Nombres. 8 (1996), 429-442. Zbl 0871.11033, MR 1438480, 10.5802/jtnb.179 |
| Reference:
|
[9] Zhang, W., Yi, Y.: On the $2m$-th power mean of certain Hardy sums.Soochow J. Math. 26 (2000), 73-84. Zbl 0999.11060, MR 1755136 |
| Reference:
|
[9] Zhang, W., Yi, Y.: On the $2m$-th power mean of certain Hardy sums.Soochow J. Math. 26 (2000), 73-84. Zbl 0999.11060, MR 1755136 |
| . |
