Zeta Functions of a Class of Artin–Schreier Curves with Many Automorphisms

Abstract

This paper describes a class of Artin–Schreier curves, generalizing results of Van der Geer and Van der Vlugt to odd characteristic. The automorphism group of these curves contains a large extraspecial group as a subgroup. Precise knowledge of this subgroup makes it possible to compute the zeta function of the curves in this class over the field of definition of all automorphisms in the subgroup.