Rankin-Cohen brackets on quasimodular forms

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 provides a Lie structure on quasimodular forms. They also satisfy a “Leibniz rule” for the usual derivation. Rankin-Cohen operators are useful for proving arithmetical identities. In particular, we explain why Chazy equation has the exact shape it has.

Article de revue

Journal of the Ramanujan Mathematical Society 24, No. 3, 213-233