Moment zeta functions for toric Calabi-Yau hypersurfaces

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 pp-adic unit rootzeta functions. In this paper, we use ll-adic cohomologyto calculate all the higher moment zeta functions for themirror 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 factorsfor the moment zeta functions.