Meromorphic continuation for the zeta function of a Dwork hypersurface

Abstract

We consider the one-parameter family of hypersurfaces in $\Pj^5$ with projective equation (X_1^5+X_2^5+X_3^5+X_4^5+X_5^5) = 5λX_1 X_2... X_5, (writing $λ$ for the parameter), proving that the Galois representations attached to their cohomologies are potentially automorphic, and hence that the zeta function of the family has meromorphic continuation throughout the complex plane.

13 pages; final version, to appear in Algebra and Number Theory. This version does not incorporate any minor changes (e.g. typographical changes) made in proof