Periods of automorphic forms: The case of (U n+1×U n ,U n )

Abstract

Abstract Following Jacquet, Lapid and Rogawski, we define regularized periods of automorphic forms on \mathrm{U}_{n+1} \times \mathrm{U}_{n} along the diagonal subgroup {\mathrm{U}_{n}} and compute the regularized periods of cuspidal Eisenstein series and their residues. The formula for the periods of residues has an application to the Gan–Gross–Prasad conjecture.