Arthur conjectures
Encyclopedia
In mathematics, the Arthur conjectures are some conjectures about automorphic representations of reductive group
s over the adele
s and unitary representation
s of reductive groups over local field
s made by , motivated by the Arthur-Selberg trace formula.
Arthur's conjectures imply the generalized Ramanujan conjectures for cusp forms on general linear groups.
Reductive group
In mathematics, a reductive group is an algebraic group G over an algebraically closed field such that the unipotent radical of G is trivial . Any semisimple algebraic group is reductive, as is any algebraic torus and any general linear group...
s over the adele
Adele
Adele is a female given name of European origin used in English, French, German and Italian with a meaning of noble, kind, and tender...
s and unitary representation
Unitary representation
In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π is a unitary operator for every g ∈ G...
s of reductive groups over local field
Local field
In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non-discrete topology.Given such a field, an absolute value can be defined on it. There are two basic types of local field: those in which the absolute value is archimedean and...
s made by , motivated by the Arthur-Selberg trace formula.
Arthur's conjectures imply the generalized Ramanujan conjectures for cusp forms on general linear groups.