On Drinfeld modular forms of higher rank II

2017/08/14 by Ernst-Ulrich Gekeler, Gekeler, Ernst-Ulrich
Mathematics · #11F52 #14G22 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F52 #msc:14G22

paper · pdf · doi:10.48550/arxiv.1708.04197

arxiv created 2017/08/14 · arxiv updated 2017/08/15

Abstract

We show that the absolute value |f| of an invertible holomorphic function f on the Drinfeld symmetric space \OM^r (r ≥ 2) is constant on fibers of the building map to the Bruhat-Tits building \MB\MT. Its logarithm log|f| is an affine map on the realization of \MB\MT. These results are used to study the vanishing loci of modular forms (coefficient forms, Eisenstein series, para-Eisenstein series) and to determine their images in \MB\MT.

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