Poisson structures and star products on quasimodular forms

François Dumas (1) , Emmanuel Royer (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We construct and classify all Poisson structures on quasimodular forms that extend the one coming from the first Rankin-Cohen bracket on the modular forms. We use them to build formal deformations on the algebra of quasimodular forms.

Mots clés: Quasimodular forms; Poisson brackets; Rankin-Cohen brackets; formal deformation; Eholzer product; star product

Domaines: Anneaux et algèbres [math.RA]; Théorie des nombres [math.NT]

François Dumas, Emmanuel Royer. Poisson structures and star products on quasimodular forms. Algebra & Number Theory, 2014, 8 (5), pp.1127-1149. ⟨hal-00834222v2⟩