Drinfeld discriminant function and Fourier expansion of harmonic cochains

2019/04/06 by Mihran Papikian, Papikian, Mihran, Fu-Tsun Wei +1
Mathematics · #11G09 #11G18 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G09 #msc:11G18

paper · pdf · doi:10.48550/arxiv.1904.03489

The paper has been significantly revised and extended

arxiv created 2020/08/05 · arxiv updated 2020/08/07

Abstract

Let F_∞=\mathbbF_q( (1/T) ) be the completion of \mathbbF_q(T) at 1/T. We develop a theory of Fourier expansions for harmonic cochains on the edges of the Bruhat-Tits building of PGL_r(F_∞), r≥ 2, generalizing an earlier construction of Gekeler for r=2. We then apply this theory to study modular units on the Drinfeld symmetric space Ω^r over F_∞, and the cuspidal divisor groups of Satake compactifications of certain Drinfeld modular varieties. In particular, we obtain a higher dimensional analogue of a result of Ogg for classical modular curves X₀(p) of prime level.

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