Second moments of Dirichlet $L$-functions weighted by Kloosterman sums

Title:

Second moments of Dirichlet $L$-functions weighted by Kloosterman sums

Creator:

Wang, Tingting

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:957d5cc9-5bfe-42e6-83e7-5fb5d17e44cd
uuid:957d5cc9-5bfe-42e6-83e7-5fb5d17e44cd

Subject:

general $k$-th Kloosterman sum, Dirichlet $L$-function, the mean square value, and asymptotic formula

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

655-661

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:3

Harvested from:

CDK

Metadata only:

false