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

JOURNAL OF NUMBER THEORY

卷:222

Article

Gekeler, Ernst-Ulrich¹ 

[1] Univ Saarland, Saarbrucken, Germany

关键词: Drinfeld modular forms;    Coefficient forms;    Eisenstein series;    Para-Eisenstein series;    Bruhat-Tits building van der Put transform;    Zero locus;   

DOI  :  10.1016/j.jnt.2020.10.007

来源: Elsevier

【 摘 要 】

This paper continues work of the earlier articles with the same title. For two classes of modular forms f: para-Eisenstein series alpha( )(k)and coefficient forms( a)l(k), where k is an element of N and a is a non-constant element of F-q[T], the growth behavior on the fundamental domain and the zero loci Omega(f) as well as their images BT(f) in the Bruhat-Tits building BT are studied. We obtain a complete description for f = alpha(k) and for those of the forms (a)l(k) where k <= deg a. It turns out that in these cases, alpha(k) and (a)l(k) are strongly related, e.g., BT((a)l(k)) = BT(alpha(k)), and that BT(alpha(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 alpha(2) in rank 3. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free