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

Wang, Tingting. "Second moments of Dirichlet $L$-functions weighted by Kloosterman sums." Czechoslovak Mathematical Journal 62.3 (2012): 655-661. <http://eudml.org/doc/246771>.

@article{Wang2012,
abstract = {For the general modulo $q\ge 3$ 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.},
author = {Wang, Tingting},
journal = {Czechoslovak Mathematical Journal},
keywords = {general $k$-th Kloosterman sum; Dirichlet $L$-function; the mean square value; asymptotic formula; general -th Kloosterman sum; Dirichlet -function; mean square value; asymptotic formula},
language = {eng},
number = {3},
pages = {655-661},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Second moments of Dirichlet $L$-functions weighted by Kloosterman sums},
url = {http://eudml.org/doc/246771},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Wang, Tingting
TI - Second moments of Dirichlet $L$-functions weighted by Kloosterman sums
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 3
SP - 655
EP - 661
AB - For the general modulo $q\ge 3$ 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.
LA - eng
KW - general $k$-th Kloosterman sum; Dirichlet $L$-function; the mean square value; asymptotic formula; general -th Kloosterman sum; Dirichlet -function; mean square value; asymptotic formula
UR - http://eudml.org/doc/246771
ER -