Communications in Number Theory and Physics

Volume 1 (2007)

Number 3

Moment zeta functions for toric Calabi–Yau hypersurfaces

Pages: 539 – 578

DOI: http://dx.doi.org/10.4310/CNTP.2007.v1.n3.a4

Authors

Antonio Rojas-Leon (Departamento de Algebra, Universidad de Sevilla, Spain)

Daqing Wan (Department of Mathematics, University of California at Irvine)

Abstract

Moment zeta functions provide a diophantineformulation for the distribution of rational points on afamily of algebraic varieties over finite fields. They also formalgebraic approximations to Dwork’s $p$-adic unit rootzeta functions. In this paper, we use $l$-adic cohomologyto calculate all the higher moment zeta functions for themirror family of the Calabi-Yau family of smooth projectivehypersurfaces over finite fields. Our main result is a completedetermination of the purity decomposition and the trivial factorsfor the moment zeta functions.

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