REMARK ON AVERAGE OF CLASS NUMBERS OF FUNCTION FIELDS
Hwanyup Jung · Korean Journal of Mathematics · 2013
Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$ , where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$ . Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$ . Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$ .