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Mirror symmetry suggests unexpected relationships between arithmeticproperties of distinct families of algebraic varieties. For example, Wan andothers have shown that for some mirror pairs, the number of rational pointsover a finite field matches modulo the order of the field. In this paper, weobtain a similar result for certain mirror pairs of toric hypersurfaces. We userecent results by Huang, Lian, Yau and Yu describing the relationship betweenthe Picard-Fuchs equations of these varieties and their Hasse--Witt matrices,which encapsulate information about the number of points. The result allows usto compute the number of points modulo the order of the field explicitly. Weillustrate this by computing K3 surface examples related to hypergeometricfunctions.

Hasse--Witt matrices and mirror toric pencils