On the change of root numbers under twisting and applications
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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.References
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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