Automorphic forms for some even unimodular lattices

Dummigan, Neil and Fretwell, Dan (2021) Automorphic forms for some even unimodular lattices. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 91 (1). pp. 29-67.

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Abstract

We look at genera of even unimodular lattices of rank 12 over the ring of integers of Q(5) and of rank 8 over the ring of integers of 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 modular forms. Turning to the genus of Hermitian lattices of rank 12 over the Eisenstein integers, even and unimodular over 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.

Item Type:
Journal Article
Journal or Publication Title:
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2600
Subjects:
?? algebraic modular formseven unimodular latticeshermitian modular formshilbert modular formstheta seriesgeneral mathematics ??
ID Code:
196904
Deposited By:
Deposited On:
17 Jul 2023 14:20
Refereed?:
Yes
Published?:
Published
Last Modified:
17 Sep 2024 09:52