On differential modular forms and some analytic relations between Eisenstein series |
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Authors: | Hossein Movasati |
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Affiliation: | (1) Instituto de Matemática Pura e Aplicada, IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, RJ, Brazil |
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Abstract: | 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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Keywords: | Modular form Hecke operator Gauss– Manin connection |
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