Limit formulas of period integrals for a certain symmetric pair II

Abstract

Let (G,H) = (U(p,q),U(p-1,q) × U(1)) and {Γ_n} a tower of congruence uniform lattices in G. By the period integrals of automorphic forms on Γ$¥backslash$G along Γ_n ∩ H$¥backslash$H, we introduce a certain discrete measure dμ_Γn^H on the H-spherical unitary dual of G. It is shown that the sequence of measures dμ_Γn^H with growing n converges in a weak sense to the Plancherel measure dμ^H for the symmetric space H$¥backslash$G.