| Title:
|
Second moments of Dirichlet $L$-functions weighted by Kloosterman sums (English) |
| Author:
|
Wang, Tingting |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
655-661 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For the general modulo $q\geq 3$ and a general multiplicative character $\chi $ modulo $q$, the upper bound estimate of $ |S(m, n, 1, \chi , q)| $ is a very complex and difficult problem. In most cases, the Weil type bound for $ |S(m, n, 1, \chi , q)| $ is valid, but there are some counterexamples. Although the value distribution of $ |S(m, n, 1, \chi , q)| $ is very complicated, it also exhibits many good distribution properties in some number theory problems. The main purpose of this paper is using the estimate for $k$-th Kloosterman sums and analytic method to study the asymptotic properties of the mean square value of Dirichlet $L$-functions weighted by Kloosterman sums, and give an interesting mean value formula for it, which extends the result in reference of W. Zhang, Y. Yi, X. He: 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. (English) |
| Keyword:
|
general $k$-th Kloosterman sum |
| Keyword:
|
Dirichlet $L$-function |
| Keyword:
|
the mean square value |
| Keyword:
|
asymptotic formula |
| MSC:
|
11L05 |
| MSC:
|
11M06 |
| MSC:
|
11M38 |
| idZBL:
|
Zbl 1265.11086 |
| idMR:
|
MR2984626 |
| DOI:
|
10.1007/s10587-012-0057-y |
| . |
| Date available:
|
2012-11-10T21:04:32Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143017 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| . |
