Triple Product L Functions and Quantum Chaos on SL(2,C)

TL;DR

This paper extends the connection between quantum unique ergodicity and subconvexity of triple product L-functions from hyperbolic surfaces to three-dimensional hyperbolic manifolds, using advanced representation theory.

Contribution

It generalizes Watson's results to SL(2,C), incorporating nonspherical automorphic forms and complex places, with new microlocal lift constructions and triple product formulas.

Findings

Established QUE for automorphic forms on hyperbolic 3-manifolds.

Linked QUE to subconvexity bounds of triple product L-functions.

Developed microlocal lifts for nonspherical automorphic forms.

Abstract

We extend the results of Watson, which link quantum unique ergodicity on arithmetic hyperbolic surfaces with subconvexity for the triple product L function, to the case of arithmetic hyperbolic three manifolds. We work with the full unitary dual of SL(2,C), and consider QUE for automorphic forms of arbitrary fixed weight and growing spectral parameter. We obtain our results by constructing microlocal lifts of nonspherical automorphic forms using representation theory, and quantifying the generalised triple product formula of Ichino in the case of complex places.