BCOV rings on elliptic curves and eta function
  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 $\eta(q^{24})$. Our method involves a classification of rational solutions of a Riccati equation under some constraints. 
So Okada
math.AG hep-th math.CA math.NT