Mirror Symmetry For Zeta Functions

Abstract

In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror. Two types of arithmetic relations are discovered. This motivates us to formulate two general arithmetic mirror conjectures for the zeta functions of a mirror pair of Calabi-Yau manifolds.

28 pages

References in corpus (1)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

Cited by in corpus (10)

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• On Witt vector cohomology for singular varieties
• Zeta Functions of Projective Toric Hypersurfaces over Finite Fields
• Moment Zeta Functions for Toric Calabi-Yau Hypersurfaces
• Counting compositions over finite abelian groups
• Congruences of the cardinalities of rational points of log Fano varieties and log Calabi-Yau varieties over the log points of finite fields
• Zeta function factorisation, Dwork hypersurfaces, hypergeometric hypersurfaces