Arthur's conjectures

January 01, 1970

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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 edit

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, ISBN 978-0-8176-3634-0, MR 1162533
Arthur, James (1989), "Unipotent automorphic representations: conjectures" (PDF), Astérisque (171): 13–71, ISSN 0303-1179, 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.: American Mathematical Society, pp. 43–93, ISBN 978-0-8218-2873-1

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January 01, 1970

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