Limit formulas of period integrals for a certain symmetric pair II

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  • Limit formulas of period integrals for a certain symmetric pair (2)

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Abstract

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

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