Arithmetic-geometric means for hyperelliptic curves and Calabi-Yau varieties

2010/01/27 by Keiji Matsumoto, Matsumoto, Keiji, Tomohide Terasoma +1
Mathematics · #14K20 #32G20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1001.4868

openalex publication_date 2010/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we define a generalized arithmetic-geometric mean μ_g among 2^g terms motivated by 2τ-formulas of theta constants. By using Thomae's formula, we give two expressions of μ_g when initial terms satisfy some conditions. One is given in terms of period integrals of a hyperelliptic curve C of genus g. The other is by a period integral of a certain Calabi-Yau g-fold given as a double cover of the g-dimensional projective space P^g.

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