Differential modular forms and some analytic relations between Eisenstein series

Details Differential modular forms and some analytic relations between Eisenstein series Differential modular forms and some analytic relations between Eisenstein series

2006-10-27

arxiv.org/abs/math/0610861v1

Mathematics

Number Theory

To appear in Ramanujan Journal

Scientific paper

In the present 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. The fact that a complex manifold over the moduli of polarized Hodge structures in the case $h^{10}=h^{01}=1$ has an algebraic structure with an action of an algebraic group plays a basic role in all of the proofs.

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