On the Existence and Temperedness of Cusp Forms for SL(3,Z)

dc.creatorMiller, Stephen D.
dc.date2000-06-08
dc.date.accessioned2026-07-07T04:35:47Z
dc.date.available2026-07-07T04:35:47Z
dc.descriptionWe 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.description47 pages, + 7 page appendix chart available at http://www.math.yale.edu/users/steve/sl3
dc.identifierhttps://arxiv.org/abs/math/0006058
dc.identifierhttp://arxiv.org/abs/math/0006058
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59372
dc.subjectNumber Theory
dc.titleOn the Existence and Temperedness of Cusp Forms for SL(3,Z)
dc.typetext

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