# Automorphic forms for some even unimodular lattices

@article{Dummigan2021AutomorphicFF, title={Automorphic forms for some even unimodular lattices}, author={Neil Dummigan and Dan Fretwell}, journal={Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg}, year={2021}, pages={1-39} }

We look at genera of even unimodular lattices of rank 12 over the ring of integers of $${{\mathbb {Q}}}(\sqrt{5})$$ Q ( 5 ) and of rank 8 over the ring of integers of $${{\mathbb {Q}}}(\sqrt{3})$$ Q ( 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…

## 2 Citations

Definite orthogonal modular forms: Computations, Excursions and Discoveries

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- 2022

. We consider spaces of modular forms attached to deﬁnite orthogonal groups of low even rank and nontrivial level, equipped with Hecke operators deﬁned by Kneser neighbours. After reviewing…

Neighbors and arithmetic of isogenous K3 surfaces

- Mathematics
- 2022

A BSTRACT . We use lattice theory to study the isogeny class of a K3 surface. Starting from isotropic Brauer classes, we construct isogenies via Kneser method of neighboring lattices. We also…

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