Jacobi Forms of Critical Weight and Weil Representations
Jacobi Forms of Critical Weight and Weil Representations
复制标题
临界重量和 Weil 表示的雅可比形式
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
N. Skoruppa
中科院分区：
文献类型：
--
作者：
N. Skoruppa
Jacobi形式可以被认为是向量值模形式，临界权的Jacobi形式对应于权为1的向量值模形式。由于SL（2，Z）的同余子群上的权为1的模形式是theta级数，所以临界权的Jacobi形式理论与有限二次模的Weil表示理论密切相关。本文详细地解释了这种关系，给出了在这方面有用的关于Weil表示的各种事实，并通过证明各种消失定理和证明关于SL（2，Z）上权为1的Jacobi形式的一个猜想，给出了本文所发展的理论的一些应用。(2000数学科目分类：11F03 11F50 11F27）
Jacobi forms can be considered as vector valued modular forms, and Jacobi forms of critical weight correspond to vector valued modular forms of weight 1 . Since the only modular forms of weight 1 on congruence subgroups of SL(2, Z) are theta series the theory of Jacobi forms of critical weight is intimately related to the theory of Weil representations of finite quadratic modules. This article explains this relation in detail, gives an account of various facts about Weil representations which are useful in this context, and it gives some applications of the theory developed herein by proving various vanishing theorems and by proving a conjecture on Jacobi forms of weight one on SL(2, Z) with character. (2000 Mathematics Subject Classification: 11F03 11F50 11F27 )