某些偶单模格的自同构形式

IF 0.4 4区 数学 Q4 MATHEMATICS
Neil Dummigan, Dan Fretwell
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引用次数: 2

摘要

我们使用Kneer邻居对标量值代数模形式的空间进行对角化,来研究\({\mathbb{Q}})(\sqrt{5})\)的整数环上的秩为12的偶数幺模格的属和\({{\math bb{Q}}}(\skrt{3})})的整数圈上秩为8的偶幺模格。我们以Ikeda和Yamana的方式推测了大多数全局Arthur参数,并使用θ级数证明了其中的几个参数。我们发现了非平行权希尔伯特模形式的同余实例。关于Eisenstein整数上秩为12的Hermitian格的亏格,({{\mathbb{Z}})上的偶和幺模,我们证明了Hentschel、Krieg和Nebe的一个猜想,将θ级数的一个线性组合确定为Hermitian Ikeda提升,并证明了另一个是Hermitian Miyawaki提升。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Automorphic forms for some even unimodular lattices

We look at genera of even unimodular lattices of rank 12 over the ring of integers of \({{\mathbb {Q}}}(\sqrt{5})\) and of rank 8 over the ring of integers of \({{\mathbb {Q}}}(\sqrt{3})\), using Kneser neighbours to diagonalise spaces of scalar-valued algebraic modular forms. We conjecture most of the global Arthur parameters, and prove several of them using theta series, in the manner of Ikeda and Yamana. We find instances of congruences for non-parallel weight Hilbert modular forms. Turning to the genus of Hermitian lattices of rank 12 over the Eisenstein integers, even and unimodular over \({{\mathbb {Z}}}\), we prove a conjecture of Hentschel, Krieg and Nebe, identifying a certain linear combination of theta series as an Hermitian Ikeda lift, and we prove that another is an Hermitian Miyawaki lift.

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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
7
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.
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