On the Existence and Temperedness of Cusp Forms for SL(3,Z)
| dc.creator | Miller, Stephen D. | |
| dc.date | 2000-06-08 | |
| dc.date.accessioned | 2026-07-07T04:35:47Z | |
| dc.date.available | 2026-07-07T04:35:47Z | |
| dc.description | We develop a partial trace formula which circumvents some technical difficulties in computing the Selberg trace formula for the quotient $SL_3({\Z})\backslash SL_3({\R})/SO_3({\R})$. As applications, we establish the Weyl asymptotic law for the discrete Laplace spectrum and prove that almost all of its cusp forms are tempered at infinity. The technique shows there are non-lifted cusp forms on $SL_3({\Z})\backslash SL_3({\R})/SO_3({\R})$ as well as non-self-dual ones. A self-contained description of our proof for $SL_2({\Z})\backslash \U$ is included to convey the main new ideas. Heavy use is made of truncation and the Maass-Selberg relations. | |
| dc.description | 47 pages, + 7 page appendix chart available at http://www.math.yale.edu/users/steve/sl3 | |
| dc.identifier | https://arxiv.org/abs/math/0006058 | |
| dc.identifier | http://arxiv.org/abs/math/0006058 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59372 | |
| dc.subject | Number Theory | |
| dc.title | On the Existence and Temperedness of Cusp Forms for SL(3,Z) | |
| dc.type | text |