Moment zeta functions for toric Calabi–Yau hypersurfaces

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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Published 1 January 2007