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

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 N∈𝔽 q [t].

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 N∈𝔽 q [t].

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1003
Classification: 11F52,  11G09
Keywords: Drinfeld modular forms, Drinfeld modules 
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Dirk Basson; Florian Breuer. On certain Drinfeld modular forms of higher rank. Journal de Théorie des Nombres de Bordeaux, Volume 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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