Critical values of L-functions of residual representations of GL₄

In this paper we prove rationality results of critical values for L-functions attached to representations in the residual spectrum of GL₄(A). We use the Jacquet-Langlands correspondence to describe their partial L-functions via cuspidal automorphic representations of the group GL₂'(A) over a quaternion algebra. Using ideas inspired by results of Grobner and Raghuram we are then able to compute the critical values as a Shalika period up to a rational multiple.