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Rankin-Cohen brackets on quasimodular forms

François Martin·Emmanuel Royer
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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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François Martin, Emmanuel Royer. 2008-04-12. Rankin-Cohen brackets on quasimodular forms. https://arxiv.org/abs/math/0509653

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