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1 LMBP - Laboratoire de Mathématiques Blaise Pascal

Abstract : We give the algebra of quasimodular forms a collection of Rankin-Cohen operators. These operators extend those defined by Cohen on modular forms and, as for modular forms, the first of them provide a Lie structure on quasimodular forms. They also satisfy a ``Leibniz rule- for the usual derivation. Rankin-Cohen operators are useful for proving arithmetic identities. In particular we give an interpretation of the Chazy equation and explain why such an equation has to exist.

keyword : Rankin-Cohen operators quasimodular forms Leibniz rule Chazy Ramanujan differential equation





Autor: François Martin - Emmanuel Royer -

Fuente: https://hal.archives-ouvertes.fr/



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