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Automorphic form

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G {\displaystyle G} to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup Γ < G {\displaystyle \Gamma <G} of the topological group. Automorphic forms are a generalization of the idea of…

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Definition

History

Automorphic representations

Poincaré on discovery and his work on automorphic functions

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Automorphic form

Nodes93
Edges92
Triples57
Avg. degree1.98
Density0.021505
Components1

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Automorphic form

Top relations

related to history · 16
Automorphic form → Before, Eisenstein, From, Fuchsian, He, Hilbert-Blumenthal, Ilya Piatetski-Shapiro, Much, Riemann, Robert Langlands, Roch, Selberg, Srinivasa Ramanujan, The, The Hilbert, The Siegel
related to Poincaré on discovery and his work on automorphic functions · 9
Automorphic form → Automorphic, Fuchs, Fuchsian, He, Lazarus Fuchs, One, Poincaré, Poincaré's, Under Poincaré's
related to Automorphic representations · 8
Automorphic form → Casimir, Hecke, Inside, It, L2, Langlands, One, The
related to References · 7
Automorphic form → Adele, Automorphic, Creative Commons Attribution/Share-Alike License, ISBN, Jules Henri Poincaré, PlanetMath, Stephen Gelbart
related to External links · 5
Automorphic form → Automorphic, Quotations, Wikimedia Commons, Wikiquote Media, Wiktionary-logo-en-v2
see also · 5
Automorphic form → Automorphic, Forms, GL, Jacquet, Robert LanglandsJacobi
related to Definition · 4
Automorphic form → Equivalently, In, Suppose, Then
is a · 3
Automorphic form → function F on G, function whose divisor is invariant under the action of G, well-behaved function from a topological group G

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Important terminology

automorphic forms group form functions function theory displaystyle groups number general invariant modular one poincaré space adelic factor langlands discrete

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Automorphic formis awell-behaved function from a topological group G0.90text
Automorphic formis afunction whose divisor is invariant under the action of G0.90text
Automorphic formis afunction F on G0.90text
Automorphic formrelated to Automorphic representationsThe0.60section
Automorphic formrelated to Automorphic representationsIt0.60section
Automorphic formrelated to Automorphic representationsInside0.60section
Automorphic formrelated to Automorphic representationsL20.60section
Automorphic formrelated to Automorphic representationsOne0.60section
Automorphic formrelated to Automorphic representationsHecke0.60section
Automorphic formrelated to Automorphic representationsCasimir0.60section
Automorphic formrelated to Automorphic representationsLanglands0.60section
Automorphic formrelated to DefinitionIn0.60section

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