期刊
RAMANUJAN JOURNAL
卷 17, 期 1, 页码 53-76出版社
SPRINGER
DOI: 10.1007/s11139-006-9009-1
关键词
modular form; Hecke operator; Gauss-Manin connection
类别
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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