Rankin Triple Products and Quantum Chaos
| dc.creator | Watson, Thomas C. | |
| dc.date | 2008-10-02 | |
| dc.date | 2008-10-22 | |
| dc.date.accessioned | 2026-07-07T10:11:59Z | |
| dc.date.available | 2026-07-07T10:11:59Z | |
| dc.description | 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. | |
| dc.description | 58 pages. A reformatted version, with minor revisions, of my Ph.D. thesis (Princeton 2002, adviser: Peter Sarnak). For the original, see 0810.0425v1. | |
| dc.identifier | https://arxiv.org/abs/0810.0425 | |
| dc.identifier | http://arxiv.org/abs/0810.0425 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172033 | |
| dc.subject | Number Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Dynamical Systems | |
| dc.subject | M11F67, 81Q50 (Primary) ;11F27, 11M26, 37A45 (Secondary) | |
| dc.title | Rankin Triple Products and Quantum Chaos | |
| dc.type | text |