Graded rings of Hermitian modular forms of degree 2
Graded rings of Hermitian modular forms of degree 2
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2 次 Hermitian 模形式的分级环
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
A. Krieg
中科院分区：
文献类型：
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作者：
Tobias Dern;A. Krieg
本文首先证明了在任意二次数域K上，任意二次Siegel模形式和偶权模形式都可以提升为二次Hermitian模形式。 在和的情形下，我们刻画了关于所有交换特征标的厄米特模形式的分次环。发电机被构造为Maaßlift或Borcherds产品。该描述允许在生成器和关系方面进行表征。此外，通过分析PSp 2（π/3 π）的五维表示，证明了分次环是由θ常数生成的.作为应用，确定了厄米特模函数的域.
Abstract At first it is shown that any Siegel modular form of degree 2 and even weight can be lifted to a Hermitian modular form of degree 2 over any imaginary-quadratic number field K. In the cases and we describe the graded rings of Hermitian modular forms with respect to all abelian characters. Generators are constructed as Maaßlifts or as Borcherds products. The description allows a characterization in terms of generators and relations. Moreover we show that the graded rings are generated by theta constants by analyzing the associated five-dimensional representation of PSp2(ℤ/3ℤ). As an application the fields of Hermitian modular functions are determined.