Mirror Symmetry For Zeta Functions

2004/11/22 by Daqing Wan, Wan, Daqing · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0411464

28 pages

arxiv created 2004/11/22 · openalex publication_date 2004/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Counting compositions over finite abelian groups
• A survey of Calabi-Yau manifolds

Related

• Equalities, congruences, and quotients of zeta functions in Arithmetic Mirror Symmetry
• The Arithmetic of Calabi--Yau Manifolds and Mirror Symmetry
• Zeta functions of alternate mirror Calabi-Yau families
• Families of Calabi-Yau manifolds and mirror symmetry
• Introduction to Arithmetic Mirror Symmetry