Two graded rings of Hermitian modular forms

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-08-12 DOI:10.1007/s12188-021-00245-z

Brandon Williams

引用次数: 4

Abstract

We give generators and relations for the graded rings of Hermitian modular forms of degree two over the rings of integers in \({\mathbb {Q}}(\sqrt{-7})\) and \({\mathbb {Q}}(\sqrt{-11})\). In both cases we prove that the subrings of symmetric modular forms are generated by Maass lifts. The computation uses a reduction process against Borcherds products which also leads to a dimension formula for the spaces of modular forms.

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厄密模形式的两个分级环

我们给出了在\（｛\mathbb｛Q｝｝（\sqrt｛-7｝）\）和\（｛｛\math bb｛Q｝（\ sqrt｛-11｝））中的整数环上二阶Hermitian模形式的分次环的生成元和关系。在这两种情况下，我们都证明了对称模形式的子环是由Maas提升生成的。计算使用了针对Borcherds乘积的归约过程，这也导致了模形式空间的维数公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.