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2010 Meromorphic continuation for the zeta function of a Dwork hypersurface
Thomas Barnet-Lamb
Algebra Number Theory 4(7): 839-854 (2010). DOI: 10.2140/ant.2010.4.839

Abstract

We consider the one-parameter family of hypersurfaces in 5 over with projective equation (X15+X25+X35+X45+X55)=5tX1X2X5, 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.

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Thomas Barnet-Lamb. "Meromorphic continuation for the zeta function of a Dwork hypersurface." Algebra Number Theory 4 (7) 839 - 854, 2010. https://doi.org/10.2140/ant.2010.4.839

Information

Received: 16 January 2009; Revised: 9 August 2010; Accepted: 10 August 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1229.14018
MathSciNet: MR2776875
Digital Object Identifier: 10.2140/ant.2010.4.839

Subjects:
Primary: 11G40
Secondary: 11F23 , 11R39

Keywords: Dwork hypersurface , potential automorphy , zeta function

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.4 • No. 7 • 2010
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