A local converse theorem for quasi-split even special orthogonal groups

Abstract

We give a direct proof of the local converse theorem for quasi-split non-split ${\mathrm{SO}}_{2l}$ over a local non-Archimedean field of characteristic $p\ne 2$, applying the theory of Howe vectors and partial Bessel functions.

arXiv admin note: substantial text overlap with arXiv:2301.13847