no. 1
Hecke operators in half-integral weight
Purkait, Soma1
1 Mathematics Institute University of Warwick Coventry CV4 7AL United Kingdom
Journal de théorie des nombres de Bordeaux, Tome 26 (2014) no. 1, pp. 233-251.

Dans [6], Shimura a introduit la notion de formes modulaires de poids demi-entier et leurs algèbres de Hecke ; il a aussi établi leur lien avec les formes modulaires de poids entier via la correspondance de Shimura. Pour les formes modulaires de poids entier, les bornes de Sturm permettent de déterminer des générateurs de l’algèbre de Hecke comme module. L’on dispose également de formules de récurrence bien connues pour les opérateurs T p ℓ en les p premiers. Le but de cet article est d’établir des résultats analogues dans le cas de poids demi-entier. Nous donnons également une formule explicite sur la commutativité des opérateurs T p ℓ avec la correspondance de Shimura.

In [6], Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence. For modular forms of integral weight, Sturm’s bounds give generators of the Hecke algebra as a module. We also have well-known recursion formulae for the operators T p ℓ with p prime. It is the purpose of this paper to prove analogous results in the half-integral weight setting. We also give an explicit formula for how operators T p ℓ commute with the Shimura correspondence.

DOI : 10.5802/jtnb.865
Classification : 11F37, 11F11
Purkait, Soma 1

1 Mathematics Institute University of Warwick Coventry CV4 7AL United Kingdom 
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Purkait, Soma. Hecke operators in half-integral weight. Journal de théorie des nombres de Bordeaux, Tome 26 (2014) no. 1, pp. 233-251. doi : 10.5802/jtnb.865. http://www.numdam.org/articles/10.5802/jtnb.865/

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