Structure of the module of vector-valued modular forms

• Autores: Christopher Marks, Geoffrey Mason
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 82, Nº 1, 2010, págs. 32-48
• Idioma: inglés
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• Resumen

  • Let V be a representation of the modular group �¡ of dimension p. We show that the Z-graded space H(V ) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra M of classical holomorphic modular forms. We study the nature of H considered as a functor from �¡-modules to graded M-lattices and give some applications, including the calculation of the Hilbert.Poincar�Le series of H(V ) in some cases.