Mathematics – Number Theory
Scientific paper
2008-10-02
Mathematics
Number Theory
58 pages. A reformatted version, with minor revisions, of my Ph.D. thesis (Princeton 2002, adviser: Peter Sarnak). For the ori
Scientific paper
We prove explicit Harris-Kudla type formulas for triples of Maass forms, holomorphic forms, and combinations thereof, on the hyperbolic plane modulo congruence groups and co-compact lattices arising from Eichler orders of quaternion algebras. These formulas relate the central value of the corresponding Rankin triple product L-function to a squared trilinear period integral. Assuming subconvexity estimates for these L-values, we prove Quantum Unique Ergodicity on such quotients; the relevant Lindelof hypotheses imply a quantitative form of QUE, with an optimal rate. In connection with the Berry/Hejhal Random Wave conjecture, we prove decay of third moments in the high energy limit, making use of a subconvexity result of Iwaniec/Ivic/Jutila and Kim-Shahidi's result on cuspidality of the symmetric cube.
No associations
LandOfFree
Rankin Triple Products and Quantum Chaos does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Rankin Triple Products and Quantum Chaos, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rankin Triple Products and Quantum Chaos will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-492505