The Langlands Parameter of a Simple Supercuspidal Representation:Odd Orthogonal Groups

In this work, we explicitly compute a certain family of twisted gamma factors of a simple supercuspidal representation π of a p-adic odd orthogonal group. These computations, together with analogous computations for general linear groups carried out in previous work with Liu [AL14], allow us to give a prediction for the Langlands parameter of π. We then prove that our prediction is correct if p is sufficiently large.