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Explicit Calculations of Automorphic Forms for Definite Unitary Groups

Published online by Cambridge University Press:  01 February 2010

David Loeffler
David Loeffler
Affiliation:
Department of Mathematics, Imperial College, South Kensington, London SW7 2AZ, United Kingdom, D.Loeffler@dpmms.cam.ac.uk

Abstract

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I give an algorithm for computing the full space of automor-phic forms for definite unitary groups over ℚ, and apply this to calculate the automorphic forms of level G(hat{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 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic form of weight (3, 3) corresponding to a family of 3-dimensional irreducible ℓ-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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 11 , 2008 , pp. 326 - 342
Copyright
Copyright © London Mathematical Society 2008

References

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Supplementary material: File

JCM 11 Loeffler Appendix A Part 1

Loeffler Appendix A Part 1

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JCM 11 Loeffler Appendix A readme

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JCM 11 Loeffler Appendix B Part 1

Loeffler Appendix B Part 1

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JCM 11 Loeffler Appendix B readme

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