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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:characterizedBy
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Analyticity
Eigenfunction of invariant differential operators
Growth condition
Transformation property under discrete group
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gptkbp:definedIn
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Locally symmetric space
Reductive algebraic group
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gptkbp:field
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gptkb:Mathematics
gptkb:Number_theory
gptkb:Representation_theory
Harmonic analysis
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gptkbp:firstAppearance
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Early 20th century
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gptkbp:generalizes
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gptkb:Hilbert_modular_form
gptkb:Maass_form
gptkb:Siegel_modular_form
gptkb:Modular_form
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gptkbp:hasApplication
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gptkb:Number_theory
gptkb:Algebraic_geometry
gptkb:Langlands_program
gptkb:Representation_theory
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gptkbp:hasProperty
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Fourier expansion
Satisfies functional equation
Analytic function
Invariance under group action
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https://www.w3.org/2000/01/rdf-schema#label
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Automorphic form
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gptkbp:notableExample
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gptkb:Maass_form
gptkb:Eisenstein_series
gptkb:Modular_form
gptkb:Theta_function
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gptkbp:relatedTo
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gptkb:Langlands_program
gptkb:Modular_form
Automorphic representation
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gptkbp:studiedBy
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gptkb:Erich_Hecke
gptkb:Robert_Langlands
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gptkbp:studiedIn
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gptkb:Langlands_program
Automorphic representation theory
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gptkbp:usedIn
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Modularity theorem
Proof of Fermat's Last Theorem
Langlands reciprocity
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gptkbp:bfsParent
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gptkb:lion
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gptkbp:bfsLayer
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4
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