#### Vol. 4, No. 7, 2010

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Meromorphic continuation for the zeta function of a Dwork hypersurface

### Thomas Barnet-Lamb

Vol. 4 (2010), No. 7, 839–854
##### Abstract

We consider the one-parameter family of hypersurfaces in ${ℙ}^{5}$ over $ℚ$ with projective equation $\left({X}_{1}^{5}+{X}_{2}^{5}+{X}_{3}^{5}+{X}_{4}^{5}+{X}_{5}^{5}\right)=5t{X}_{1}{X}_{2}\dots {X}_{5}$, proving that the Galois representations attached to their cohomologies are potentially automorphic, and hence that the zeta function of the family has meromorphic continuation to the whole complex plane.

##### Keywords
Dwork hypersurface, potential automorphy, zeta function
##### Mathematical Subject Classification 2000
Primary: 11G40
Secondary: 11R39, 11F23