On the converse theorem for Borcherds products

被引：37
作者：
Bruinier, Jan Hendrik [1 ]
机构：
[1] Tech Univ Darmstadt, Fachbereich Math, D-64289 Darmstadt, Germany
来源：
JOURNAL OF ALGEBRA | 2014年 / 397卷
关键词：
Automorphic form; Theta function; Borcherds product; Picard group; AUTOMORPHIC-FORMS; VARIETIES;
D O I：
10.1016/j.jalgebra.2013.08.034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a new converse theorem for Borcherds' multiplicative theta lift which improves the previously known results. To this end we develop a newform theory for vector valued modular forms for the Weil representation, which might be of independent interest. We also derive lower bounds for the ranks of the Picard groups and the spaces of holomorphic top degree differential forms of modular varieties associated to orthogonal groups. (C) 2013 Elsevier Inc. All rights reserved.
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页码：315 / 342
页数：28
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