BCOV rings on elliptic curves and eta function

2016/01/29 by So Okada, Okada, So
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Rings, Modules, and Algebras #hep-th #math.AG #math.CA #math.NT

paper · pdf · doi:10.48550/arxiv.1601.08029

arxiv created 2016/01/29 · openalex publication_date 2016/01/29 · arxiv updated 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Associated Legendre functions of the first kind give a family of BCOV rings on elliptic curves. We prove that the family is parametrized by q-exponents of the eta function η(q²⁴). Our method involves a classification of rational solutions of a Riccati equation under some constraints.

Related

• BCOV ring and holomorphic anomaly equation
• Chudnovsky-Ramanujan Type Formulae for the Legendre Family
• A method for construction of rational points over elliptic curves
• Explicit points on the Legendre curve
• Elliptic Curves, eta-quotients, and hypergeometric functions