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Formes quasi-modulaires sur des groupes modulaires
co-compacts et restrictions des formes modulaires
de Hilbert aux courbes modulaires.

Abstract : We prove a structure theorem for the
graded ring $\widetilde{M}_*(\Gamma)$ of
quasi-modular forms over any discrete and cocompact
group $\Gamma \subset \rm{PSL}(2, \mathbb{R}).$
This ring is not finitely generated. We calculate
the exact number of new generators of weight $k.$
This number is constant and equals $\dim_{\mathbb{C}}
I / (I \cap \widetilde{I}^2),$ where $I$ and
$\widetilde{I}$ are the ideal of modular forms
and the ideal of quasi-modular forms, of positive
weights. So, this number depend only on the group
$\Gamma.$ We construct also finitely generated rings
of positive weights which contain the rings of
quasi-modular forms over modular cocompact groups.
We study also restrictions of Hilbert modular
forms to modular curves : we prove that the space
generated by a sequence of restrictions of
Hilbert modular forms to a modular curve
is a subspace closed under
Rankin-Cohen brakets of the space of modular
forms over the modular curve.
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https://tel.archives-ouvertes.fr/tel-00011122
Contributor : Najib Ouled Azaiez <>
Submitted on : Sunday, November 27, 2005 - 9:01:58 PM
Last modification on : Wednesday, December 9, 2020 - 3:09:37 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:36:12 PM

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  • HAL Id : tel-00011122, version 1

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Najib Ouled Azaiez. Formes quasi-modulaires sur des groupes modulaires
co-compacts et restrictions des formes modulaires
de Hilbert aux courbes modulaires.. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00011122⟩

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