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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:definedIn
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gptkb:Upper_half-plane
|
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gptkbp:field
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gptkb:Mathematics
|
|
gptkbp:generalizes
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gptkb:Hilbert_modular_form
gptkb:Siegel_modular_form
gptkb:Automorphic_form
|
|
gptkbp:hasApplication
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gptkb:Algebraic_geometry
gptkb:string_theory
Cryptography
Mathematical physics
Moonshine theory
|
|
gptkbp:hasCuspForm
|
Yes
|
|
gptkbp:hasEisensteinSeries
|
Yes
|
|
gptkbp:hasFourierExpansion
|
Yes
|
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gptkbp:hasProperty
|
gptkb:Hecke_operator
gptkb:lion
gptkb:Petersson_inner_product
gptkb:Congruence_subgroup
gptkb:Modular_curve
q-expansion
Transformation law
Fourier coefficients
Character (Dirichlet character)
Growth condition
Holomorphic at infinity
Level (N)
Modular symbol
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|
gptkbp:hasSpecialCase
|
gptkb:Eisenstein_series
Cusp form
Modular function
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|
gptkbp:hasSubfield
|
gptkb:Number_theory
Complex analysis
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Modular form
|
|
gptkbp:isHolomorphic
|
Yes
|
|
gptkbp:relatedTo
|
gptkb:Modular_group
gptkb:Automorphic_form
Elliptic curve
Modular function
|
|
gptkbp:studiedBy
|
gptkb:Yutaka_Taniyama
gptkb:André_Weil
gptkb:Erich_Hecke
gptkb:Henri_Poincaré
gptkb:Goro_Shimura
|
|
gptkbp:transformsUnder
|
gptkb:SL(2,_Z)
|
|
gptkbp:usedIn
|
gptkb:Langlands_program
Proof of Fermat's Last Theorem
Theory of L-functions
|
|
gptkbp:weight
|
k (integer or half-integer)
|
|
gptkbp:bfsParent
|
gptkb:lion
|
|
gptkbp:bfsLayer
|
4
|