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Equivariant Forms: Structure and Geometry

Published:2012-02-03
Printed: Sep 2013
• Abdelkrim Elbasraoui,
Centre de recherches mathématiques, Université de Montréal, C.P. 6128, Succursale Centre Ville, Montréal, Québec
• Abdellah Sebbar,
Department of Mathematics and Statistics, University of Ottawa, Ottawa Ontario
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Abstract

In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of $\operatorname{SL}_2(\mathbb{Z})$ by means of the cross-ratio, the weight 2 modular forms, the quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.
 Keywords: equivariant forms, modular forms, Schwarz derivative, cross-ratio, differential forms
 MSC Classifications: 11F11 - Holomorphic modular forms of integral weight