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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.

• 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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