Meromorphic continuation for the zeta function of a Dwork hypersurface

2008/11/10 by Barnet-Lamb, Thomas · 1 citation
#11F23 #11G40 #11R39 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0811.1588

Abstract

We consider the one-parameter family of hypersurfaces in \Pj⁵ with projective equation (X₁⁵+X₂⁵+X₃⁵+X₄⁵+X₅⁵) = 5λX₁ X₂... X₅, (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.

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• The residual monodromy for the Dwork family in even characteristic and its applications to Galois representations

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