  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 functions of
the curves in the class over the field of definition of all automorphisms in
the subgroup. As a consequence, we obtain new examples of maximal curves.
