Experimental Mathematics

Computing Genus-$2$ Hilbert--Siegel Modular Forms over $\Q(\sqrt{5})$ via the Jacquet--Langlands Correspondence

Clifton Cunningham and Lassina Dembélé

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Abstract

In this paper we present an algorithm for computing Hecke eigensystems of Hilbert--Siegel cusp forms over real quadratic fields of narrow class number one. We give some illustrative examples using the quadratic field $\Q(\sqrt{5})$. In those examples, we identify Hilbert--Siegel eigenforms that are possible lifts from Hilbert eigenforms.

Article information

Source
Experiment. Math., Volume 18, Issue 3 (2009), 337-345.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.em/1259158470

Mathematical Reviews number (MathSciNet)
MR2555703

Zentralblatt MATH identifier
1246.11102

Subjects
Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]

Keywords
Hilbert--Siegel modular forms Jacquet--Langlands correspondence Brandt matrices Satake parameters

Citation

Cunningham, Clifton; Dembélé, Lassina. Computing Genus-$2$ Hilbert--Siegel Modular Forms over $\Q(\sqrt{5})$ via the Jacquet--Langlands Correspondence. Experiment. Math. 18 (2009), no. 3, 337--345. https://projecteuclid.org/euclid.em/1259158470


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