Rankin-Cohen brackets on quasimodular forms
François Martin, Emmanuel Royer
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.
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