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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2013
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| 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: |
| Sumario: | 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. |
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