Meromorphic continuation for the zeta function of a Dwork hypersurface

Details Meromorphic continuation for the zeta function of a Dwork hypersurface Meromorphic continuation for the zeta function of a Dwork hypersurface

2008-11-10

arxiv.org/abs/0811.1588v3

Mathematics

Number Theory

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

Scientific paper

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) = 5\lambda X_1 X_2... X_5, (writing $\lambda$ 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.

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