On the residue method for period integrals

Abstract

By applying the residue method for period integrals, we prove identities between period integrals on cuspidal automorphic representations and period integrals on residual representations for seven spherical varieties. Combining this with the Langlands–Shahidi theory for residues of Eisenstein series, for each case, we prove some relations between the period integrals and certain automorphic L-functions. In some cases, we also study the local multiplicity of the spherical varieties.