On the ramification of modular parametrizations at the cusps - ENS de Lyon - École normale supérieure de Lyon Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

On the ramification of modular parametrizations at the cusps

François Brunault
  • Fonction : Auteur
  • PersonId : 923270

Résumé

We investigate the ramification of modular parametrizations of elliptic curves over $\Q$ at the cusps. We prove that if the modular form associated to the elliptic curve has minimal level among its twists by Dirichlet characters, then the modular parametrization is unramified at the cusps. The proof uses Bushnell's formula for the Godement-Jacquet local constant of a cuspidal automorphic representation of $\GL(2)$. We also report on numerical computations indicating that in general, the ramification index at a cusp seems to be a divisor of 24.
Fichier principal
Vignette du fichier
ephi.pdf (414.88 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

ensl-00707488 , version 1 (12-06-2012)
ensl-00707488 , version 2 (13-12-2018)

Identifiants

Citer

François Brunault. On the ramification of modular parametrizations at the cusps. 2012. ⟨ensl-00707488v1⟩
75 Consultations
203 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More