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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the change of root numbers under twisting and applications
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by Ariel Pacetti PDF
Proc. Amer. Math. Soc. 141 (2013), 2615-2628 Request permission

Abstract:

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.
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Additional Information
  • Ariel Pacetti
  • Affiliation: Departamento de Matemática, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, CP 1428, Buenos Aires, Argentina
  • MR Author ID: 759256
  • Email: apacetti@dm.uba.ar
  • Received by editor(s): October 20, 2010
  • Received by editor(s) in revised form: November 8, 2011
  • Published electronically: April 24, 2013
  • Additional Notes: The first author was partially supported by PIP 2010-2012 GI and UBACyT X113
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2615-2628
  • MSC (2010): Primary 11F70
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11532-7
  • MathSciNet review: 3056552