On the mean values of $L(1,\chi)$
Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1303-1310
Printed November 30, 2012
Zhaoxia Wu and Wenpeng Zhang
Northwest University, Northwest University
Abstract : Let $p>2$ be a prime, and let $k\geq 1$ be an integer.Let $\chi$ be a Dirichlet character modulo $p$, and let $L(s,\chi)$ be the Dirichlet $L$-functions corresponding to $\chi$. In this paper we consider the mean values of $$ \mathop{\sum_{\chi\bmod p}}_{\chi(-1)=-1}\chi(2^k)\left|L(1,\chi)\right|^2. $$
Keywords : $L$-function, Dirichlet character, identity
MSC numbers : 11M06
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