Arthur’s multiplicity formula for even orthogonal and unitary groups

Abstract

Let $F$ be a number field and $G$ an even orthogonal or unitary group over a number field. Based on the method used by Gan and Ichino (2018), we prove Arthur’s multiplicity formula for the generic part of the automorphic discrete spectrum of $G$ by using the theta lift. Enhancing this method, we also obtain a description of the full automorphic discrete spectrum of $G$ of $F$-rank $\le 1$.