Dummigan, N. and Fretwell, D. (2021) Automorphic forms for some even unimodular lattices. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 91 (1). pp. 29-67. ISSN 0025-5858
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Authors. This is an author-produced version of a paper subsequently published in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Algebraic modular forms; even unimodular lattices; theta series; Hilbert modular forms; Hermitian modular forms |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 26 Jan 2021 07:55 |
Last Modified: | 20 Feb 2022 01:38 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s12188-021-00231-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:170076 |