Heat equation for theta functions and vector-valued modular forms

被引：0
|
作者：
Perna, Sara [1 ]
机构：
[1] Leibniz Univ Hannover, Inst Algebra Geometrie, Welfengarten 1, D-30167 Hannover, Germany
来源：
MANUSCRIPTA MATHEMATICA | 2018年 / 157卷 / 1-2期
关键词：
HOLOMORPHIC DIFFERENTIAL FORMS;
D O I：
10.1007/s00229-017-0980-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a method for constructing vector-valued modular forms from singular scalar-valued ones of a suitable type. As an application, we prove that two remarkable spaces of vector-valued modular forms, which seem to be unrelated at a first look since they are constructed in two very different ways, are the same. More precisely, let V-grad be the vector space generated by vector-valued modular forms constructed with gradients of odd theta functions and let V-Theta be the one generated by vector-valued modular forms arising from second order theta constants with our construction. We will prove that V-grad = V-Theta.
引用
收藏
页码：81 / 99
页数：19
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