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Explicit calculations of automorphic forms for definite unitary groups
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Loeffler, David (2008) Explicit calculations of automorphic forms for definite unitary groups. LMS Journal of Computation and Mathematics, Vol.11 . pp. 326-342. doi:10.1112/S1461157000000620 ISSN 1461-1570.
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Official URL: http://dx.doi.org/10.1112/S1461157000000620
Abstract
I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level G(^Z) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 x U1 x U1 and U1 x U2, and to an example of a non-endoscopic form of weight (3; 3) corresponding to a family of 3-dimensional irreducible 2-adic Galois representations. I also compute the 2-adic slopes of some automorphic forms with level structure at 2, giving evidence for the local constancy of the slopes.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Unitary groups, Automorphic forms | ||||
Journal or Publication Title: | LMS Journal of Computation and Mathematics | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 1461-1570 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.11 | ||||
Page Range: | pp. 326-342 | ||||
DOI: | 10.1112/S1461157000000620 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
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