| Title:
|
An identity involving Dedekind sums and generalized Kloosterman sums (English) |
| Author:
|
Huan, Le |
| Author:
|
Wang, Jingzhe |
| Author:
|
Wang, Tingting |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
991-1001 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums $K(m, n, r; q)$. The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid mean value involving Dedekind sums and generalized Kloosterman sums, and give an interesting identity. (English) |
| Keyword:
|
Dedekind sum |
| Keyword:
|
Kloosterman sum |
| Keyword:
|
Dirichlet character |
| Keyword:
|
analytic method |
| Keyword:
|
Gauss sum |
| Keyword:
|
identity |
| MSC:
|
11F20 |
| MSC:
|
11L05 |
| MSC:
|
11M20 |
| MSC:
|
11N37 |
| idZBL:
|
Zbl 1259.11089 |
| idMR:
|
MR3010252 |
| DOI:
|
10.1007/s10587-012-0078-6 |
| . |
| Date available:
|
2012-11-10T21:36:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143040 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] 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:
|
[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] Estermann, T.: On Kloostermann's sums.Mathematika, Lond. 8 (1961), 83-86. MR 0126420, 10.1112/S0025579300002187 |
| Reference:
|
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| Reference:
|
[7] Liu, Y., Zhang, W.: A hybrid mean value related to the Dedekind sums and Kloosterman sums.Sci. China, Math. 53 (2010), 2543-2550; Acta Math. Sin. 27 (2011), 435-440 MR 2718846, 10.1007/s11425-010-3153-1 |
| Reference:
|
[8] 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:
|
[9] Zhang, W.: A sum analogous to Dedekind sums and its hybrid mean value formula.Acta Arith. 107 (2003), 1-8. Zbl 1126.11317, MR 1956981, 10.4064/aa107-1-1 |
| . |
