Triple product L-functions and quantum chaos on SL(2, ℂ)

Abstract

Let Y be an arithmetic hyperbolic 3-manifold. We establish a link between quantum unique ergodicity for sections of automorphic vector bundles on Y and subconvexity for the triple product L-function, which extends a result of Watson in the case of hyperbolic 2-manifolds. The proof combines the representation theoretic microlocal lift for bundles developed by Bunke and Olbrich with the triple product formula of Ichino. A key step is determining the asymptotic behaviour of the local integrals at complex places that appear in Ichino’s formula.