On Drinfeld modular forms of higher rank V: The behavior of distinguished forms on the fundamental domain

2020/09/03 by Gekeler, Ernst-Ulrich
#11F23 #11F52 #11F85 #14G22 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2009.01622

Abstract

\begindocument \begin This paper continues work of the earlier articles with the same title. For two classes of modular forms f: \beginitemize \item para-Eisenstein series α_k and \item coefficient forms _a ℓ_k, where k ∈ ℕ and a is a non-constant element of \mathbbF_q[T], \enditemize the growth behavior on the fundamental domain and the zero loci Ω(f) as well as their images BT(f) in the Bruhat-Tits building BT are studied. We obtain a complete description for f = α_k and for those of the forms _aℓ_k where k ≤ °a. It turns out that in these cases, α_k and _aℓ_k are strongly related, e.g., BT(_aℓ_k) = BT(α_k), and that BT(α_k) is the set of ℚ-points of a full subcomplex of BT with nice properties. As a case study, we present in detail the outcome for the forms α₂ in rank 3. \endabstract \maketitle \enddocument

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