Periods of residual automorphic forms

We develop a technique for computing period integrals of noncuspidal automorphic forms. Applications include a formula for the integral of a square-integrable automorphic form on GLn(AE)GLn(AE) over GLn(F)\GLn(AF)1GLn(F)\GLn(AF)1 for a quadratic extension E of a number field F and a characterization of residual automorphic representations on which the period integral is nonvanishing.