Rankin-Cohen brackets on quasimodular forms

2005/09/28 by François Martin, Martin, François, Emmanuel Royer +1 · 1 citation
Mathematics · #11F11 #11F22 #16W25 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F22 #msc:16W25

paper · pdf · doi:10.48550/arxiv.math/0509653

17 pages

openalex publication_date 2005/09/28 · arxiv created 2008/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Quasimodular forms, Jacobi-like forms, and pseudodifferential operators

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