Mirror Symmetry For Zeta Functions
Daqing Wan
TL;DR
This paper explores the relationship between zeta functions of Calabi-Yau hypersurfaces and their mirrors, proposing new conjectures on their arithmetic connections based on observed relations.
Contribution
It introduces two novel arithmetic mirror conjectures linking the zeta functions of mirror Calabi-Yau manifolds.
Findings
Discovered two types of arithmetic relations between zeta functions
Formulated two general arithmetic mirror conjectures
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds