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arXiv · 1208.2633

A Note on the Mean Value of $L$--functions in Function Fields

Julio Andrade
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Abstract

An asymptotic formula for the sum $\sum L(1,\chi)$ is established for a family of hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_q$ as $g\rightarrow\infty$ making use of the analogue of the approximate functional equation for such $L$--functions. As a corollary, we obtain a formula for the average of the class number of the associated rings $\mathbb{F}_{q}[T,sqrt{D}]$.

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Julio Andrade. 2012-08-13. A Note on the Mean Value of $L$--functions in Function Fields. https://arxiv.org/abs/1208.2633

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