Bulletin of the
Korean Mathematical Society BKMS

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