Formal deformations of the algebra of Jacobi forms and Rankin-Cohen brackets
29 juin 2021·
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0 min. de lecture
YoungJu Choie
François Dumas
François Martin

Emmanuel Royer
Résumé
The aim of this work is to emphasize the arithmetical and algebraic aspects of the Rankin-Cohen brackets in order to extend them to several natural number-theoretical situations. We build an analytically consistent derivation on the algebra of weak Jacobi forms. From this derivation, we obtain a sequence of bilinear forms on that is a formal deformation and whose restriction to the algebra of modular forms is an analogue of Rankin-Cohen brackets associated to the Serre derivative. Using a classification of all admissible Poisson brackets, we generalize this construction to build a family of Rankin-Cohen deformations of . The algebra is a polynomial algebra in four generators. We consider some localization of with respect to one of the generators. We construct Rankin-Cohen deformations on . We study their restriction to and to some subalgebra of naturally isomorphic to the algebra of quasimodular forms.
Type
Publication
Comptes rendus mathématiques de l’Académie des sciences de Paris 359, No. 4, 505-521