Arthur's conjectures
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In mathematics, the Arthur conjectures are some conjectures about
automorphic representations of reductive groups over the adeles and unitary representations of reductive groups over local fields made by James Arthur (1989), motivated by the Arthur–Selberg trace formula
.
Arthur's conjectures imply the
generalized Ramanujan conjectures
for cusp forms on general linear groups.
References
- Adams, Jeffrey; Barbasch, Dan; Vogan, David A. (1992), The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Boston, MA: Birkhäuser Boston, MR 1162533
- Arthur, James (1989), "Unipotent automorphic representations: conjectures" (PDF), Astérisque (171): 13–71, MR 1021499
- Clozel, Laurent (2007), "Spectral theory of automorphic forms", in Sarnak, Peter; Shahidi, Freydoon (eds.), Automorphic forms and applications, IAS/Park City Math. Ser., vol. 12, Providence, R.I.: ISBN 978-0-8218-2873-1
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