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| HAL : hal-00009145, version 2 |
| arXiv : math/0509653 |
| Fiche détaillée |  Récupérer au format |
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| Journal of the Ramanujan Mathematical Society 24, 3 (2009) 213-233 |
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| Versions disponibles : | v1 (28-09-2005) | v2 (12-04-2008) |
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| Rankin-Cohen brackets on quasimodular forms |
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| François Martin 1Emmanuel Royer 1 |
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| Modunombres (ANR), Nomex (BQR Université Blaise Pascal) Collaboration(s) |
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| (2009) |
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| We give the algebra of quasimodular forms a collection of Rankin-Cohen operators. These operators extend those defined by Cohen on modular forms and, as for modular forms, the first of them provide a Lie structure on quasimodular forms. They also satisfy a ``Leibniz rule'' for the usual derivation. Rankin-Cohen operators are useful for proving arithmetic identities. In particular we give an interpretation of the Chazy equation and explain why such an equation has to exist. |
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| 1 : | Laboratoire de Mathématiques |
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CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II |
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| Théorie des nombres et analyse, UMR 6620 |
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| Domaine | : | Mathématiques/Théorie des nombres |
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| Rankin-Cohen operators – quasimodular forms – Leibniz rule – Chazy – Ramanujan – differential equation |
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| hal-00009145, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00009145 | |
| oai:hal.archives-ouvertes.fr:hal-00009145 | |
| Contributeur : Emmanuel Royer | |
| Soumis le : Samedi 12 Avril 2008, 11:25:12 | |
| Dernière modification le : Jeudi 25 Mars 2010, 20:14:10 | |
