| Title:
|
On the mean value of a sum analogous to character sums over short intervals (English) |
| Author:
|
Ganglian, Ren |
| Author:
|
Wenpeng, Zhang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
651-668 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main purpose of this paper is to study the mean value properties of a sum analogous to character sums over short intervals by using the mean value theorems for the Dirichlet L-functions, and to give some interesting asymptotic formulae. (English) |
| Keyword:
|
character sums |
| Keyword:
|
short intervals |
| Keyword:
|
even power mean |
| Keyword:
|
asymptotic formula |
| MSC:
|
11L40 |
| idZBL:
|
Zbl 1174.11067 |
| idMR:
|
MR2455928 |
| . |
| Date available:
|
2010-07-20T13:57:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140411 |
| . |
| Reference:
|
[1] Pólya, G.: Über die Verteilung der quadratische Reste und Nichtreste.Göttingen Nachrichten (1918), 21-29. |
| Reference:
|
[2] Vinogradov, I. M.: On the distribution of residues and non-residues of powers.Journal of the Physico-Mathematical society of Perm 1 (1918), 94-96. |
| Reference:
|
[3] Sokolovskiĭ, A. V.: On a theorem of Sárkozy.Acta Arithmetica 41 (1982), 27-31. MR 0667707 |
| Reference:
|
[4] Burgess, D. A.: On a conjecture of Norton.Acta Arithmetica 27 (1975), 265-267. Zbl 0258.10018, MR 0364125, 10.4064/aa-27-1-265-267 |
| Reference:
|
[5] Xu, Zhefeng, Zhang, Wenpeng: On the $2k$th power mean of the character sums over short intervals.Acta Arithmetica 121 (2006), 149-160. Zbl 1153.11046, MR 2216139, 10.4064/aa121-2-4 |
| Reference:
|
[6] Peral, Juan C.: Character sums and explicit estimates for L-functions.Contemporary Mathematics 189 (1995), 449-459. Zbl 0837.11045, MR 1347030, 10.1090/conm/189/02280 |
| Reference:
|
[7] Zhang, Wenpeng: On a Cochrane sum and its hybrid mean value formula (II).Journal of Mathematical Analysis and Applications 276 (2002), 446-457. Zbl 1106.11304, MR 1944361, 10.1016/S0022-247X(02)00501-2 |
| Reference:
|
[8] Zhang, Wenpeng, Yi, Yuan, He, Xiali: On the $2k$-th power mean of Dirichlet $L$-functions with the weight of general Kloosterman sums.Journal of Number Theory 84 (2000), 199-213. Zbl 0958.11061, MR 1795790, 10.1006/jnth.2000.2515 |
| Reference:
|
[9] He, Xiali, Zhang, Wenpeng: On the mean value of Dedekind sums.Acta Mathematica 15 (1999), 245-254. MR 1714067, 10.1007/BF02650668 |
| . |
