In mathematics, the Arthur conjectures are some conjectures about
automorphic representation
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset ...
s of
reductive groups over the
adeles and
unitary representations of reductive groups over
local fields made by , motivated by the
Arthur–Selberg trace formula.
Arthur's conjectures imply the
generalized Ramanujan conjectures for cusp forms on general linear groups.
References
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Automorphic forms
Representation theory
Conjectures
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