On the change of root numbers under twisting and applications

The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can, for each odd prime p, determine whether a modular form (or a Hilbert modular form) with triv...

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Autor principal: Pacetti, A.
Formato: JOUR
Materias:
Local factors
Twisting epsilon factors
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v141_n8_p2615_Pacetti
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00029939_v141_n8_p2615_Pacetti
record_format dspace
spelling todo:paper_00029939_v141_n8_p2615_Pacetti2023-10-03T13:55:14Z On the change of root numbers under twisting and applications Pacetti, A. Local factors Twisting epsilon factors The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can, for each odd prime p, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is either Steinberg, principal series or supercuspidal at p by analyzing the change of sign under a suitable twist. We also explain the case p = 2, where twisting, in general, is not enough. © 2012 American Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v141_n8_p2615_Pacetti
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Local factors
Twisting epsilon factors
spellingShingle Local factors
Twisting epsilon factors
Pacetti, A.
On the change of root numbers under twisting and applications
topic_facet Local factors
Twisting epsilon factors
description The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can, for each odd prime p, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is either Steinberg, principal series or supercuspidal at p by analyzing the change of sign under a suitable twist. We also explain the case p = 2, where twisting, in general, is not enough. © 2012 American Mathematical Society.
format JOUR
author Pacetti, A.
author_facet Pacetti, A.
author_sort Pacetti, A.
title On the change of root numbers under twisting and applications
title_short On the change of root numbers under twisting and applications
title_full On the change of root numbers under twisting and applications
title_fullStr On the change of root numbers under twisting and applications
title_full_unstemmed On the change of root numbers under twisting and applications
title_sort on the change of root numbers under twisting and applications
url http://hdl.handle.net/20.500.12110/paper_00029939_v141_n8_p2615_Pacetti
work_keys_str_mv AT pacettia onthechangeofrootnumbersundertwistingandapplications
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