2005/06/06 by Hossein Movasati, Movasati, Hossein
Mathematics · #14 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14
paper · pdf · doi:10.48550/arxiv.math/0506106
arxiv created 2005/06/06 · openalex publication_date 2005/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we define the algebra of differential modular forms and we prove that it is generated by Eisenstein series of weight 2,4 and 6. We define Hecke operators on them, find some analytic relations between these Eisenstein series and obtain them in a natural way as coefficients of a family of elliptic curves. Then we describe the relation between the dynamics of a foliation in \C3 induced by the Ramanujan relations, with vanishing of elliptic integrals. The fact that a complex manifold over the Moduli of Polarized Hodge Structures in the case h10=h01=1 has an algebraic structure with an action of an algebraic group plays a basic role in all of the proofs.