Number theory
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Representation theory
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Lie group
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Harmonic analysis
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Discrete groups
Automorphic form
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 o...
Hypergeometric function
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Modular form
Hypergeometric function
In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific ...
Modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also...
Kampé de Fériet function
In mathematics, the Kampé de Fériet function is a two-variable generalization of the hypergeometric series, introduced by Marie-Joseph Kampé de Fériet.The Kampé de Fériet function is given by
Hypergeometric identity
In mathematics, hypergeometric identities are equalities involving sums over hypergeometric terms, i.e. the coefficients occurring in hypergeometric series. These identities occur frequently in soluti...
Hypergeometric function of a matrix argument
In mathematics, the hypergeometric function of a matrix argument is a generalization of the classical hypergeometric series. It is a function defined by an infinite summation which can be used to eval...
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 ...
Gauss's continued fraction
In complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions known to mathem...
Gauss's continued fraction - Wikipedia
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).
Langlands–Shahidi method
Multiplicity-one theorem
In the mathematical theory of automorphic representations, a multiplicity-one theorem is a result about the representation theory of an adelic reductive algebraic group. The multiplicity in question i...
Local trace formula
Langlands dual
In representation theory, a branch of mathematics, the Langlands dual G of a reductive algebraic group G (also called the L-group of G) is a group that controls the representation theory of G. If G is...
Koecher–Maass series
Ending lamination theorem
In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston (1982), states that hyperbolic 3-manifolds with finitely generated fundamental groups are det...
List of hypergeometric identities
Below is a list of hypergeometric identities.
List of hypergeometric identities - Wikipedia
Converse theorem
In the mathematical theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to be the Mellin transform of a modular form. More generally a converse theorem s...
Meijer G-function
In mathematics, the G-function was introduced by Cornelis Simon Meijer (1936) as a very general function intended to include most of the known special functions as particular cases. This was ...
Overconvergent modular form
In mathematics, overconvergent modular forms are special p-adic modular forms that are elements of certain p-adic Banach spaces (usually infinite dimensional) containing classical spaces of modular f...
Siegel upper half-space
In mathematics, the Siegel upper half-space of degree g (or genus g) (also called the Siegel upper half-plane) is the set of g × g symmetric matrices over the complex numbers whose imaginary...
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...
P-adic modular form
In mathematics, a p-adic modular form is a p-adic analog of a modular form, with coefficients that are p-adic numbers rather than complex numbers. Serre (1973) introduced p-adic modular forms as limit...
Lax pair
In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential equation, called the Lax equation. Lax pairs...
Drinfeld upper half plane
Arthur–Selberg trace formula
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...
Legendre function
In mathematics, the Legendre functions Pλ, Qλ and associated Legendre functions Pμλ, Qμλ are generalizations of Legendre polynomials to non-integer degree.
Associated Legendre ...
MacRobert E function
In mathematics, the E-function was introduced by Thomas Murray MacRobert (1937–38) to extend the generalized hypergeometric series pFq(·) to the case p > q + 1. The underlying objective w...
Factor of automorphy
In mathematics, the notion of factor of automorphy arises for a group acting on a complex-analytic manifold. Suppose a group acts on a complex-analytic manifold . Then, also acts on the space of hol...
Geometric finiteness
In geometry, a group of isometries of hyperbolic space is called geometrically finite if it has a well-behaved fundamental domain. A hyperbolic manifold is called geometrically finite if it can be d...
Bers slice
In the mathematical theory of Kleinian groups, Bers slices and Maskit slices, named after Lipman Bers and Bernard Maskit, are certain slices through the moduli space of Kleinian groups.
For a q...