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Verfasst von:Böckle, Gebhard [VerfasserIn]   i
 Gräf, Peter Mathias [VerfasserIn]   i
 Perkins, Rudolph [VerfasserIn]   i
Titel:A Hecke-equivariant decomposition of spaces of Drinfeld cusp forms via representation theory, and an investigation of its subfactors
Verf.angabe:Gebhard Böckle, Peter Mathias Gräf and Rudolph Perkins
E-Jahr:2021
Jahr:07 June 2021
Umfang:50 S.
Fussnoten:Gesehen am 29.10.2021
Titel Quelle:Enthalten in: Research in number theory
Ort Quelle:Heidelberg : Springer, 2015
Jahr Quelle:2021
Band/Heft Quelle:7(2021), 3, Artikel-ID 44, Seite 1-50
ISSN Quelle:2363-9555
Abstract:There are various reasons why a naive analog of the Maeda conjecture has to fail for Drinfeld cusp forms. Focussing on double cusp forms and using the link found by Teitelbaum between Drinfeld cusp forms and certain harmonic cochains, we observed a while ago that all obvious counterexamples disappear for certain Hecke-invariant subquotients of spaces of Drinfeld cusp forms of fixed weight, which can be defined naturally via representation theory. The present work extends Teitelbaum’s isomorphism to an adelic setting and to arbitrary levels, it makes precise the impact of representation theory, it relates certain intertwining maps to hyperderivatives of Bosser-Pellarin, and it begins an investigation into dimension formulas for the subquotients mentioned above. We end with some numerical data for $$A={\mathbb {F}}_3[t]$$that displays a new obstruction to an analog of a Maeda conjecture by discovering a conjecturally infinite supply of $${\mathbb {F}}_3(t)$$-rational eigenforms with combinatorially given (conjectural) Hecke eigenvalues at the prime t.
DOI:doi:10.1007/s40993-021-00254-0
URL:kostenfrei: Volltext: https://doi.org/10.1007/s40993-021-00254-0
 kostenfrei: Volltext: https://link.springer.com/article/10.1007/s40993-021-00254-0
 DOI: https://doi.org/10.1007/s40993-021-00254-0
Datenträger:Online-Ressource
Sprache:eng
K10plus-PPN:1775703991
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