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

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

2010-06-16

arxiv.org/abs/1006.3303v2

Mathematics

Number Theory

28 pages, submitted

Scientific paper

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.

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