On the computation of algebraic modular forms on compact inner forms of 𝐆𝐒𝐩₄-Reference-Cited by-同舟云学术

On the computation of algebraic modular forms on compact inner forms of 𝐆𝐒𝐩₄

Published:2014-01-16 Issue:288 Volume:83 Page:1931-1950
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Dembélé Lassina

Abstract

In this paper, we describe an algorithm for computing algebraic modular forms on compact inner forms of G S p 4 \mathrm {GSp}_4 over totally real number fields. By analogues of the Jacquet-Langlands correspondence for G L 2 \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 Q ( 2 ) \mathbb {Q}(\sqrt {2}) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2014-83-288/S0025-5718-2014-02374-0/S0025-5718-2014-02374-0.pdf

Reference23 articles.

1. Augmentation du niveau pour 𝑈(3);Bellaïche, Joël;Amer. J. Math.,2006

2. The Magma algebra system. I. The user language;Bosma, Wieb;J. Symbolic Comput.,1997

3. Base change for the Saito-Kurokawa representations of 𝑃𝐺𝑆𝑝(4);Cogdell, J. W.;J. Number Theory,1988

4. Tensor products of Hermitian lattices;Coulangeon, Renaud;Acta Arith.,2000

5. Computing genus-2 Hilbert-Siegel modular forms over ℚ(√5) via the Jacquet-Langlands correspondence;Cunningham, Clifton;Experiment. Math.,2009

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