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Dirk Basson; Florian Breuer
On certain Drinfeld modular forms of higher rank
Journal de théorie des nombres de Bordeaux, 29 no. 3 (2017), p. 827-843, doi: 10.5802/jtnb.1003
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Class. Math.: 11F52, 11G09
Keywords: Drinfeld modular forms, Drinfeld modules

Résumé - Abstract

We give an introduction to Drinfeld modular forms for principal congruence subgroups of $\mathrm{GL}_r(\mathbb{F}_q[t])$, 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 $N\in \mathbb{F}_q[t]$.

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