Computing Genus-$2$ Hilbert--Siegel Modular Forms over $\Q(\sqrt{5})$ via the Jacquet--Langlands Correspondence
Cunningham, Clifton ; Dembélé, Lassina
Experiment. Math., Tome 18 (2009) no. 1, p. 337-345 / Harvested from Project Euclid
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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.
Publié le : 2009-05-15
Classification:  Hilbert--Siegel modular forms,  Jacquet--Langlands correspondence,  Brandt matrices,  Satake parameters,  11F41 
@article{1259158470,
     author = {Cunningham, Clifton and Demb\'el\'e, Lassina},
     title = {Computing Genus-$2$ Hilbert--Siegel Modular Forms over $\Q(\sqrt{5})$ via the Jacquet--Langlands Correspondence},
     journal = {Experiment. Math.},
     volume = {18},
     number = {1},
     year = {2009},
     pages = { 337-345},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1259158470}
}

Cunningham, Clifton; Dembélé, Lassina. Computing Genus-$2$ Hilbert--Siegel Modular Forms over $\Q(\sqrt{5})$ via the Jacquet--Langlands Correspondence. Experiment. Math., Tome 18 (2009) no. 1, pp.  337-345. http://gdmltest.u-ga.fr/item/1259158470/