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, 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