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On the change of root numbers under twisting and applications

Author: Ariel Pacetti
Journal: Proc. Amer. Math. Soc. 141 (2013), 2615-2628
MSC (2010): Primary 11F70
Published electronically: April 24, 2013
MathSciNet review: 3056552
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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.

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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

Keywords: Local factors, twisting epsilon factors
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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