On Drinfeld modular forms of higher rank
Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 875-902.

Nous étudions les formes modulaires pour le groupe Γ=GL(r,𝔽 q [T]) sur l’espace symétrique Ω r de Drinfeld, où r2. Parmi nos résultats, on a l’existence d’une racine (q-1)-ième (à une constante près) h de la fonction discriminant Δ, la description de la (dé-)croissance des formes élémentaires g 1 ,g 2 ,,g r-1 ,Δ dans le domaine fondamental de Γ, et la réduction de ces formes sur la partie centrale o de . Nous étudions avec plus de détail le cas de r=3.

We study Drinfeld modular forms for the modular group Γ=GL(r,𝔽 q [T]) on the Drinfeld symmetric space Ω r , where r2. Results include the existence of a (q-1)-th root (up to constants) h of the discriminant function Δ, the description of the growth/decay of the standard forms g 1 ,g 2 ,g r-1 , Δ on the fundamental domain of Γ, and the reduction of these forms on the central part o of . The results are exemplified in detail for r=3.

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DOI : https://doi.org/10.5802/jtnb.1005
Classification : 11F52,  11G09,  14G22
Mots clés : Drinfeld modular forms, Drinfeld discriminant function; Bruhat–Tits building
@article{JTNB_2017__29_3_875_0,
     author = {Ernst-Ulrich Gekeler},
     title = {On {Drinfeld} modular forms of higher rank},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {875--902},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {3},
     year = {2017},
     doi = {10.5802/jtnb.1005},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1005/}
}
Ernst-Ulrich Gekeler. On Drinfeld modular forms of higher rank. Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 875-902. doi : 10.5802/jtnb.1005. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1005/

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