Mirror Symmetry For Zeta Functions

Details Mirror Symmetry For Zeta Functions Mirror Symmetry For Zeta Functions

2004-11-22

arxiv.org/abs/math/0411464v1

Mathematics

Algebraic Geometry

28 pages

Scientific paper

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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