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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:application
|
gptkb:Prime_number_theorem
gptkb:Algebraic_geometry
gptkb:Representation_theory
Modularity theorem
Reciprocity laws
Arithmetic geometry
Langlands reciprocity
Quantum chaos
|
|
gptkbp:definedIn
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Function fields
Number fields
|
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gptkbp:field
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gptkb:Number_theory
gptkb:Automorphic_forms
|
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gptkbp:firstDefined
|
20th century
|
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gptkbp:generalizes
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gptkb:Hecke_L-functions
gptkb:Artin_L-functions
gptkb:Dirichlet_L-functions
gptkb:Hasse–Weil_L-functions
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|
https://www.w3.org/2000/01/rdf-schema#label
|
Automorphic L-functions
|
|
gptkbp:notableConjecture
|
gptkb:Birch_and_Swinnerton-Dyer_conjecture
gptkb:Artin_conjecture
gptkb:Langlands_functoriality_conjecture
gptkb:Sato–Tate_conjecture
gptkb:Generalized_Ramanujan_conjecture
|
|
gptkbp:originatedIn
|
gptkb:Automorphic_forms
Automorphic representations
Adelic groups
Reductive algebraic groups
|
|
gptkbp:property
|
gptkb:Generalized_Riemann_hypothesis
gptkb:Euler_product
gptkb:Ramanujan_conjecture
Functional equation
Analytic continuation
Special values
Non-vanishing
|
|
gptkbp:relatedTo
|
gptkb:Eisenstein_series
gptkb:Langlands_program
gptkb:Modular_forms
gptkb:Zeta_functions
Galois representations
Automorphic representations
|
|
gptkbp:studiedBy
|
gptkb:Peter_Sarnak
gptkb:Robert_Langlands
gptkb:James_Arthur
gptkb:Gérard_Laumon
gptkb:Stephen_Gelbart
gptkb:Dinakar_Ramakrishnan
gptkb:Pierre_Deligne
gptkb:Hervé_Jacquet
gptkb:Henryk_Iwaniec
gptkb:Ilya_Piatetski-Shapiro
gptkb:Freydoon_Shahidi
gptkb:Joseph_Shalika
|
|
gptkbp:bfsParent
|
gptkb:Base_Change_for_GL(2)
|
|
gptkbp:bfsLayer
|
5
|