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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Detalles Bibliográficos
Publicado: 2013
Materias:
Local factors
Twisting epsilon factors
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n8_p2615_Pacetti
http://hdl.handle.net/20.500.12110/paper_00029939_v141_n8_p2615_Pacetti
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029939_v141_n8_p2615_Pacetti
record_format dspace
spelling paper:paper_00029939_v141_n8_p2615_Pacetti2023-06-08T14:23:33Z On the change of root numbers under twisting and applications 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. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n8_p2615_Pacetti 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
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.
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
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n8_p2615_Pacetti
http://hdl.handle.net/20.500.12110/paper_00029939_v141_n8_p2615_Pacetti
_version_ 1768544157130817536

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