Lifting of Modular Forms
Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 5-20.

The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group G, for any representation ρ:GGL d () of finite image can be established by lifting scalar-valued modular forms of the finite index subgroup ker(ρ) of G. In this article vvmf are explicitly constructed for any admissible multiplier (representation) ρ, see Section 3 for the definition of admissible multiplier. In other words, the following question has been partially answered: For which representations ρ of a given G, is there a vvmf with at least one nonzero component?

L’existence et construction de formes modulaires vectorielles (vvmf) pour un groupe Fuchsien arbitraire G et pour une représentation ρ:GGL d () d’image finie peut être établie en relevant des formes modulaires scalaires pour le sous-groupe d’indice fini ker(ρ) de G. Dans cet article, des vvmf sont explicitement construites pour tout multiplicateur admissible (représentation) ρ (voir paragraphe 3 pour la définition du multiplicateur admissible). En d’autres termes, on a partiellement répondu à la question suivante : Pour quelles représentations ρ d’un groupe G donné, existe-t-il une vvmf avec au moins une composante non nulle ?

Published online:
DOI: 10.5802/pmb.27
Classification: 11F03, 11F55, 30F35
Keywords: Fuchsian group, Vector-valued modular form, Induced representation

Jitendra Bajpai 1

1 Mathematisches Institut, Georg-August Universität Göttingen, D-37073 Germany.
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jitendra Bajpai. Lifting of Modular Forms. Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 5-20. doi : 10.5802/pmb.27.

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