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.

Neil Dummigan

Dan Fretwell

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

第一期“ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITÄT HAMBURG”于 1921 年出版。这本国际数学期刊从那时起为重要的研究贡献提供了一个论坛。该杂志涵盖了纯数学的所有核心领域，例如代数、复分析和几何、微分几何和全局分析、图论和离散数学、李理论、数论和代数拓扑。

The first issue of "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in 1921. Since then, this international mathematics journal has provided a forum for significant research contributions. The journal covers all core areas of pure mathematics, including algebra, complex analysis, geometry, differential geometry, global analysis, graph theory, discrete mathematics, Lie theory, number theory, and algebraic topology.

《Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg》第一期于1921年出版。这本国际数学期刊自创刊以来，为重要的研究成果提供了一个交流平台。期刊涵盖了纯数学的各个核心领域，包括代数、复分析、几何、微分几何、全局分析、图论、离散数学、李理论、数论和代数拓扑等。

Category	Quartile
数学	4
数学, 数学	4

Automorphic forms for some even unimodular lattices

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