Rankin-Cohen brackets on quasimodular forms

Details Rankin-Cohen brackets on quasimodular forms Rankin-Cohen brackets on quasimodular forms

2005-09-28

arxiv.org/abs/math/0509653v2

Mathematics

Number Theory

17 pages

Scientific paper

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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