Rankin-Cohen brackets on quasimodular forms

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.

arXiv comment17 pages

References in corpus (1)

• Rankin-Cohen Brackets and van der Pol-Type Identities for the Ramanujan's Tau Function

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