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Moment zeta functions for toric Calabi–Yau hypersurfaces


Moment zeta functions provide a diophantine formulation for the distribution of rational points on a family of algebraic varieties over finite fields. They also form algebraic approximations to Dwork's p-adic unit root zeta functions. In this paper, we use l-adic cohomology to calculate all the higher moment zeta functions for the mirror family of the Calabi-Yau family of smooth projective hypersurfaces over finite fields. Our main result is a complete determination of the purity decomposition and the trivial factors for the moment zeta functions.

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