We give an introduction to Drinfeld modular forms for principal congruence subgroups of , and then construct a rank analogue of the -function. We show that this function is a cusp form of weight and type 1 which satisfies a product formula. Along the way, we compute the expansion at infinity of weight one Eisenstein series of level .
Nous donnons une introduction aux formes modulaires de Drinfeld pour des sous-groupes de congruence principaux de , et puis nous construisons un analogue en rang de la fonction . Nous montrons que cette fonction est cuspidale de poids 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 .
Revised:
Accepted:
Published online:
Classification: 11F52, 11G09
Keywords: Drinfeld modular forms, Drinfeld modules
@article{JTNB_2017__29_3_827_0, author = {Dirk Basson and Florian Breuer}, title = {On certain {Drinfeld} modular forms of higher rank}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {827--843}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {29}, number = {3}, year = {2017}, doi = {10.5802/jtnb.1003}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1003/} }
TY - JOUR TI - On certain Drinfeld modular forms of higher rank JO - Journal de Théorie des Nombres de Bordeaux PY - 2017 DA - 2017/// SP - 827 EP - 843 VL - 29 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1003/ UR - https://doi.org/10.5802/jtnb.1003 DO - 10.5802/jtnb.1003 LA - en ID - JTNB_2017__29_3_827_0 ER -
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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