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Formal deformations of the algebra of Jacobi forms and Rankin-Cohen brackets

Abstract : This work is devoted to the algebraic and arithmetic properties of Rankin-Cohen brackets allowing to define and study them in several natural situations of number theory. It focuses on the property of these brackets to be formal deformations of the algebras on which they are defined, with related questions on restriction-extension methods. The general algebraic results developed here are applied to the study of formal deformations of the algebra of weak Jacobi forms and their relation with the Rankin-Cohen brackets on modular and quasimodular forms.
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https://hal.archives-ouvertes.fr/hal-01673663
Contributor : Emmanuel Royer Connect in order to contact the contributor
Submitted on : Friday, February 5, 2021 - 4:44:48 PM
Last modification on : Monday, July 19, 2021 - 4:42:12 PM

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  • HAL Id : hal-01673663, version 2
  • ARXIV : 1801.00582

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Youngju Choie, François Dumas, François Martin, Emmanuel Royer. Formal deformations of the algebra of Jacobi forms and Rankin-Cohen brackets. Comptes Rendus. Mathématique, Centre Mersenne (2020-..) ; Elsevier Masson (2002-2019), 2021, 359 (4), pp.505-521. ⟨hal-01673663v2⟩

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