Philippe Goutet
Published 2009-07-21Version 1
In this article, we give a proof of the link between the zeta function of two families of hypergeometric curves and the zeta function of a family of quintics that was observed numerically by Candelas, de la Ossa, and Rodriguez Villegas. The method we use is based on formulas of Koblitz and various Gauss sums identities; it does not give any geometric information on the link.
Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$-adic cohomology
Isotypic Decomposition of the Cohomology and Factorization of the Zeta Functions of Dwork Hypersurfaces
Zeta function and cryptographic exponent of supersingular curves of genus 2
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