Meromorphic continuation for the zeta function of a Dwork hypersurface
Number Theory
2010-12-07 v3
Abstract
We consider the one-parameter family of hypersurfaces in 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 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.
Keywords
Cite
@article{arxiv.0811.1588,
title = {Meromorphic continuation for the zeta function of a Dwork hypersurface},
author = {Thomas Barnet-Lamb},
journal= {arXiv preprint arXiv:0811.1588},
year = {2010}
}
Comments
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