Explicit calculations of automorphic forms for definite unitary groups
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
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|
|Page Range:||pp. 326-342|
|Access rights to Published version:||Open Access|
1. Don Blasius and Jonathan D. Rogawski, 'Tate classes and arithmetic quotients of the two-ball.' 'The zeta functions of Picard modular surfaces,' (Univ. Montréal, 1992) pp. 421-444.
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