Abstract
In this paper we study the arithmetic of Artin–Schreier extensions of \(\mathbb {F}_{q}(T)\). We determine the integral closure of \(\mathbb {F}_{q}[T]\) in Artin–Schreier extension of \(\mathbb {F}_{q}(T)\). We also investigate the average values of the \(L\)-functions of orders of Artin–Schreier extensions and study the average values of ideal class numbers when \(p=3\) in detail.
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