On Drinfeld modular forms of higher rank II

JOURNAL OF NUMBER THEORY

卷:232

Article

关键词: Drinfeld modular forms;    Bruhat-Tits building;    Eisenstein series;   

DOI  :  10.1016/j.jnt.2018.11.011

来源: Elsevier

【 摘 要 】

We show that the absolute value vertical bar f vertical bar of an invertible holomorphic function f on the Drinfeld symmetric space Omega(r) (r >= 2) is constant on fibers of the building map to the Bruhat-Tits building BT. Its logarithm log vertical bar f vertical bar is an affine map on the realization of BT. 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 BT. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free