On the change of root numbers under twisting and applications

Details On the change of root numbers under twisting and applications On the change of root numbers under twisting and applications

2010-10-19

arxiv.org/abs/1010.3781v1

Mathematics

Number Theory

15 pages

Scientific paper

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 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 is not enough in general.

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