Mystery
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Unsolved problems
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Open problem
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Mathematical problem
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Unsolved problems in mathematics
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Function (mathematics)
Conjecture
Number theory
List of unsolved problems in mathematics
Representation theory
Representation of a Lie group
Automorphic form
Zeta and L-functions
Langlands program
In mathematics, the Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algeb...
Theta correspondence
In mathematics, the theta correspondence or Howe correspondence is a correspondence between automorphic forms associated to the two groups of a dual reductive pair, introduced by Howe (1979).
Kirillov model
In mathematics, the Kirillov model, studied by Kirillov (1963), is a realization of a representation of GL2 over a local field on a space of functions on the local field.If G is the algebraic gro...
Fundamental lemma (Langlands program)
In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups. It was c...
L-packet
In the field of mathematics known as representation theory, an L-packet is a collection of (isomorphism classes of) irreducible representations of a reductive group over a local field, that are L-indi...
Local Langlands conjectures
In mathematics, the local Langlands conjectures, introduced by Langlands (1967, 1970), are part of the Langlands program. They describe a correspondence between the complex representations of a ...
Lafforgue's theorem
In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic ...
Picard modular surface
Endoscopic group
In mathematics, endoscopic groups of reductive algebraic groups were introduced by Robert Langlands (1979, 1983) in his work on the stable trace formula.Roughly speaking, an endoscopic group ...
Automorphic L-function
In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic form π of a reductive group G over a global field and a finite-dimensional comple...
Base change lifting
In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation of restricting a representation of a Galo...