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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. 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 |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of 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 |
| Date: | 2008 |
| Volume: | Vol.11 |
| Page Range: | pp. 326-342 |
| Identification Number: | 10.1112/S1461157000000620 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Open Access |
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| URI: | http://wrap.warwick.ac.uk/id/eprint/37251 |
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