On The Langlands parameter of a simple supercuspidal representation: even orthogonal groups

Let π be a simple supercuspidal representation of the split even special orthogonal group. We compute the Rankin-Selberg γ-factors for rank 1-twists of π by quadratic tamely ramified characters of F*. Our results determine certain 1-dimensional summands of the Langlands parameter. Assuming an expected analogue of a work of Blondel, Henniart, and Stevens, these summands completely determine the Langlands parameter of π.