论文标题
一些甚至单型格的自动形式
Automorphic forms for some even unimodular lattices
论文作者
论文摘要
我们查看$ \ Mathbb {q}（\ sqrt {5}）$的整数上$ 12 $的偶像晶格的属和$ 8 $的属，$ \ mathbb {q}（Q}（\ sqrt {3}）$，使用kneserer neker，$ 8 $代数模块化形式。我们猜想了大多数全球Arthur参数，并以Ikeda和Yamana的方式使用Theta系列证明了其中一些。我们发现非平行重量Hilbert模块化形式的一致性实例。 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.
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.
