On the Zeta Function of a Family of Quintics Goutet, Philippe

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Goutet, Philippe
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Journal of Number Theory
mathematics - number theory; 14g10 (primary), 11g25 (secondary), 14g15, 11t24; zeta function factorization
To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jnt.2009.11.001 Byline: Philippe Goutet Keywords: Quintic threefold; Hypergeometric curves; Zeta function factorization Abstract: 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. Author Affiliation: IMJ, case 247, 4 place Jussieu, 75252 Paris Cedex 05, France Article History: Received 31 May 2007; Revised 4 November 2009 Article Note: (miscellaneous) Communicated by Fernando Rodriguez Villegas
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