| Title:
|
On the mean value of Dedekind sum weighted by the quadratic Gauss sum (English) |
| Author:
|
Wang, Tingting |
| Author:
|
Zhang, Wenpeng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
357-367 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to study the computational problem of one kind of mean value involving the classical Dedekind sum and the quadratic Gauss sum, and give several exact computational formulae for it. (English) |
| Keyword:
|
Dedekind sum |
| Keyword:
|
quadratic Gauss sum |
| Keyword:
|
mean value |
| Keyword:
|
identity |
| MSC:
|
11F20 |
| MSC:
|
11L40 |
| idZBL:
|
Zbl 06236415 |
| idMR:
|
MR3073962 |
| DOI:
|
10.1007/s10587-013-0021-5 |
| . |
| Date available:
|
2013-07-18T14:50:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143316 |
| . |
| Reference:
|
[1] Apostol, T. M.: Introduction to Analytic Number Theory.Springer, New York (1976). Zbl 0335.10001, MR 0434929 |
| Reference:
|
[2] Apostol, T. M.: Modular Functions and Dirichlet Series in Number Theory.Springer, New York (1976). Zbl 0332.10017, MR 0422157 |
| 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] Hua, L. K.: Introduction to Number Theory.Science Press, Peking Chinese (1964). Zbl 0221.10002, MR 0194380 |
| Reference:
|
[5] 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:
|
[6] Rademacher, H.: On the transformation of $\log \eta(\tau)$.J. Indian Math. Soc., n. Ser. 19 (1955), 25-30. Zbl 0064.32703, MR 0070660 |
| Reference:
|
[7] Rademacher, H., Grosswald, E.: Dedekind Sums.The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C. (1972). Zbl 0251.10020, MR 0357299 |
| Reference:
|
[8] Weil, A.: On some exponential sums.Proc. Natl. Acad. Sci. USA 34 (1948), 204-207. Zbl 0032.26102, MR 0027006, 10.1073/pnas.34.5.204 |
| Reference:
|
[9] 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:
|
[10] 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 |
| . |
