Residual spectrum of odd orthogonal groups (Q2764648)

The purpose of this paper is fourfold. First, the author studies the Rankin-Selberg \(L\)-function of generic cuspidal representations of \(\text{GL}_k \times \text{GL}_{2l+1}\) defined over a number field, and proves that for \(k>1\), these \(L\)-functions are holomorphic except for possibly at \(s = 0,1\). The second result is the determination of the residual spectrum of \(\text{SO}_{2n+1}\) corresponding to the Eisenstein series associated with a maximal parabolic. To do this, the Langlands functorial lift from \(\text{SO}_{2n+1}\) to \(\text{GL}_{2n}\) is applied. Third, the author describes the residual spectrum of \(\text{SO}_{5}\) and \(\text{GSp}_{4}\) defined over a number field. Finally, under some assumptions the author gives a conjectural description of the residual spectrum of \(\text{SO}_{2n+1}\) coming from arbitrary parabolic subgroups.