Reference : Genuine Bianchi modular forms of higher level, at varying weight and discriminant
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/29493
Genuine Bianchi modular forms of higher level, at varying weight and discriminant
English
Rahm, Alexander mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Tsaknias, Panagiotis [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
In press
Journal de Théorie des Nombres de Bordeaux
Université de Bordeaux III
Yes (verified by ORBilu)
International
1246-7405
Talence
France
[en] Bianchi modular forms are automorphic forms over an imaginary quadratic field, associated to a Bianchi group. Those of the cuspidal Bianchi modular forms which are relatively well understood, namely (twists of) base-change forms and CM-forms, are what we call non-genuine forms; the remaining forms are what we call genuine. In a preceding paper by Rahm and Şengün, an extreme paucity of genuine forms has been reported, but those and other computations were restricted to level One. In this paper, we are extending the formulas for the non-genuine
Bianchi modular forms to higher levels, and we are able to spot the first, rare instances of genuine forms at higher level and higher weight.
[fr] Les formes modulaires de Bianchi sont des formes automorphes sur un corps quadratique imaginaire, associés à un groupe de Bianchi. Ceux parmis les formes modulaires de Bianchi cuspidales que l’on comprend relativement bien, c’est-à-dire les (twists de) formes obtenus par changement de base et formes CM, sont ce que nous appelons les formes non génuines; et nous appelons les formes qui restent les formes génuines. Dans un travail précédent par Rahm et Şengün, il a été constaté que les formes génuines sont extrêmement rares, mais ces caculs étaient restraints au niveau des groupes de Bianchi entiers. Dans ce travail, nous étendons les formules pour les formes de Bianchi non génuines à des niveaux plus hauts, et nous sommes capables d’observer les premièrs, rares, exemples de formes génuines à niveau élevé et poids élevé.
Gabor Wiese's FNR project and Gabor Wiese's University of Luxembourg grant AMFOR.
Researchers
http://hdl.handle.net/10993/29493
FnR ; FNR6543139 > Gabor Wiese > COMFGREP > Computational aspects of modular forms and p-adic Galois representations > 01/08/2013 > 31/07/2016 > 2012

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