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On the computation of algebraic modular forms on compact inner forms of $ \mathbf{GSp}_4$


Author: Lassina Dembélé
Journal: Math. Comp. 83 (2014), 1931-1950
MSC (2010): Primary 11Fxx, 11Gxx, 11Yxx
DOI: https://doi.org/10.1090/S0025-5718-2014-02374-0
Published electronically: January 16, 2014
MathSciNet review: 3194136
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Abstract: In this paper, we describe an algorithm for computing algebraic modular forms on compact inner forms of $ \mathrm {GSp}_4$ over totally real number fields. By analogues of the Jacquet-Langlands correspondence for $ \mathrm {GL}_2$, this algorithm in fact computes Hecke eigensystems of Hilbert-Siegel modular forms of genus 2. We give some examples of such eigensystems over $ \mathbb{Q}(\sqrt {2})$.


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Additional Information

Lassina Dembélé
Affiliation: Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: l.dembele@warwick.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-2014-02374-0
Received by editor(s): November 7, 2007
Received by editor(s) in revised form: October 14, 2009, and June 12, 2012
Published electronically: January 16, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.