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Automorphic forms for some even unimodular lattices

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Automorphic forms for some even unimodular lattices. / Dummigan, Neil; Fretwell, Dan.
In: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg , Vol. 91, No. 1, 30.04.2021, p. 29-67.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dummigan, N & Fretwell, D 2021, 'Automorphic forms for some even unimodular lattices', Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg , vol. 91, no. 1, pp. 29-67. https://doi.org/10.1007/s12188-021-00231-5

APA

Dummigan, N., & Fretwell, D. (2021). Automorphic forms for some even unimodular lattices. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg , 91(1), 29-67. https://doi.org/10.1007/s12188-021-00231-5

Vancouver

Dummigan N, Fretwell D. Automorphic forms for some even unimodular lattices. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg . 2021 Apr 30;91(1):29-67. Epub 2021 Feb 20. doi: 10.1007/s12188-021-00231-5

Author

Dummigan, Neil ; Fretwell, Dan. / Automorphic forms for some even unimodular lattices. In: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg . 2021 ; Vol. 91, No. 1. pp. 29-67.

Bibtex

@article{020d00caaf6945dbb339b89634756c6e,
title = "Automorphic forms for some even unimodular lattices",
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.",
keywords = "Algebraic modular forms, Even unimodular lattices, Hermitian modular forms, Hilbert modular forms, Theta series",
author = "Neil Dummigan and Dan Fretwell",
year = "2021",
month = apr,
day = "30",
doi = "10.1007/s12188-021-00231-5",
language = "English",
volume = "91",
pages = "29--67",
journal = "Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg ",
number = "1",

}

RIS

TY - JOUR

T1 - Automorphic forms for some even unimodular lattices

AU - Dummigan, Neil

AU - Fretwell, Dan

PY - 2021/4/30

Y1 - 2021/4/30

N2 - 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.

AB - 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.

KW - Algebraic modular forms

KW - Even unimodular lattices

KW - Hermitian modular forms

KW - Hilbert modular forms

KW - Theta series

U2 - 10.1007/s12188-021-00231-5

DO - 10.1007/s12188-021-00231-5

M3 - Journal article

VL - 91

SP - 29

EP - 67

JO - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

IS - 1

ER -