On certain Drinfeld modular forms of higher rank
Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 827-843.

Nous donnons une introduction aux formes modulaires de Drinfeld pour des sous-groupes de congruence principaux de GL r (𝔽 q [t]), et puis nous construisons un analogue en rang r de la fonction h. Nous montrons que cette fonction est cuspidale de poids (q r -1)/(q-1) et de type 1 et qu’elle satisfait une formule de produit. Dans ce but, nous calculons le développement à l’infini des séries d’Eisenstein de poids 1 et de nivaux N𝔽 q [t].

We give an introduction to Drinfeld modular forms for principal congruence subgroups of GL r (𝔽 q [t]), and then construct a rank r analogue of the h-function. We show that this function is a cusp form of weight (q r -1)/(q-1) and type 1 which satisfies a product formula. Along the way, we compute the expansion at infinity of weight one Eisenstein series of level N𝔽 q [t].

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DOI : 10.5802/jtnb.1003
Classification : 11F52, 11G09
Mots clés : Drinfeld modular forms, Drinfeld modules
Dirk Basson 1 ; Florian Breuer 1

1 Stellenbosch University, Stellenbosch, South Africa
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Dirk Basson; Florian Breuer. On certain Drinfeld modular forms of higher rank. Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 827-843. doi : 10.5802/jtnb.1003. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1003/

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