| Title:
|
On the $2k$-th power mean of $\frac {L'}L(1,\chi )$ with the weight of Gauss sums (English) |
| Author:
|
Ren, Dongmei |
| Author:
|
Yi, Yuan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
781-789 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main purpose of this paper is to study the hybrid mean value of $\frac {L'}L(1,\chi )$ and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the hybrid mean value $\sum _{\chi \neq \chi _0} |\tau (\chi )| |\frac {L'}L(1,\chi )|^{2k}$ of $\frac {L'}L$ and Gauss sums will be proved using analytic methods and estimates for trigonometric sums. (English) |
| Keyword:
|
Dirichlet L-function |
| Keyword:
|
Gauss sums |
| Keyword:
|
asymptotic formula |
| MSC:
|
11L07 |
| MSC:
|
11M20 |
| idZBL:
|
Zbl 1204.11140 |
| idMR:
|
MR2545656 |
| . |
| Date available:
|
2010-07-20T15:39:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140516 |
| . |
| Reference:
|
[1] Apostol, Tom M.: Introduction to Analytic Number Theory.Springer-Verlag, New York (1976), 160-162. Zbl 0335.10001, MR 0434929 |
| Reference:
|
[2] Chengdong, Pan, Chengbiao, Pan: Element of the Analytic Number Theory.Science Press, Beijing (1991), 243-248. |
| Reference:
|
[3] Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory.Springer-Verlag, New York (1982), 88-91. Zbl 0482.10001, MR 0661047 |
| Reference:
|
[4] Yuan, Yi, Wenpeng, Zhang: On the first power mean of Dirichlet L-functions with the weight of Gauss sums.Journal of Systems Science and Mathematical Sciences 20 (2000), 346-351. MR 1790030 |
| Reference:
|
[5] Yuan, Yi, Wenpeng, Zhang: On the $2k$-th Power mean of Dirichlet L-function with the weight of Gauss sums.Advances in Mathematics 31 (2002), 517-526. MR 1959549 |
| Reference:
|
[6] Davenport, H.: Multiplicative Number Theory.Springer-Verlag, New York (1980). Zbl 0453.10002, MR 0606931 |
| Reference:
|
[7] Wenpeng, Zhang: A new mean value formula of Dirichlet's L-function.Science in China (Series A) 35 (1992), 1173-1179. MR 1223064 |
| Reference:
|
[8] Huaning, Liu, Xiaobeng, Zhang: On the mean value of $\frac{L'}L(1,\chi)$.Journal of Mathematical Analysis and Applications 320 (2006), 562-577. MR 2225976 |
| Reference:
|
[9] Siegel, C. L.: Über die Klassenzahl quadratischer Zahlkörper.Acta. Arith. 1 (1935), 83-86. Zbl 0011.00903, 10.4064/aa-1-1-83-86 |
| Reference:
|
[10] Chengdong, Pan, Chengbiao, Pan: The Elementary Number Theory.Peking University Press, Beijing (2003). |
| . |
