On differential modular forms and some analytic relations between Eisenstein series

被引：10

作者：

Movasati, Hossein ^{[1
]}

机构：

[1] IMPA, Inst Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

来源：

RAMANUJAN JOURNAL | 2008年 / 17卷 / 01期

关键词：

modular form; Hecke operator; Gauss-Manin connection;

D O I：

10.1007/s11139-006-9009-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：53 / 76

页数：24

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