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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:application
|
gptkb:Langlands_program
Proof of Fermat's Last Theorem
Partition function
|
|
gptkbp:category
|
gptkb:Automorphic_forms
Holomorphic functions
Special functions
|
|
gptkbp:definedIn
|
gptkb:Upper_half-plane
|
|
gptkbp:dimensions
|
Finite
|
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gptkbp:field
|
gptkb:Mathematics
|
|
gptkbp:firstAppearance
|
19th century
|
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gptkbp:FourierExpansion
|
q-expansion
|
|
gptkbp:generalizes
|
gptkb:Cusp_forms
gptkb:Hilbert_modular_forms
gptkb:Siegel_modular_forms
|
|
gptkbp:hasCharacter
|
gptkb:lion
|
|
gptkbp:hasInvariant
|
Modular transformations
|
|
gptkbp:hasRingStructure
|
Yes
|
|
gptkbp:hasSubfield
|
gptkb:Number_theory
Complex analysis
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Modular forms
|
|
gptkbp:level
|
Positive integer
|
|
gptkbp:notableExample
|
gptkb:Eisenstein_series
Delta function
|
|
gptkbp:notablePublication
|
gptkb:Ramanujan's_tau_function
Hecke's theory of modular forms
|
|
gptkbp:relatedTo
|
gptkb:Taniyama-Shimura_conjecture
gptkb:Jacobi_forms
gptkb:Modular_curves
gptkb:Modular_functions
gptkb:Automorphic_forms
gptkb:Maass_forms
gptkb:Ramanujan_conjecture
Modularity theorem
L-functions
Galois representations
Elliptic curves
Theta functions
|
|
gptkbp:studiedBy
|
gptkb:Yutaka_Taniyama
gptkb:André_Weil
gptkb:Erich_Hecke
gptkb:Srinivasa_Ramanujan
gptkb:Goro_Shimura
|
|
gptkbp:symmetry
|
gptkb:SL(2,_Z)
|
|
gptkbp:transformationProperty
|
gptkb:Modular_group
|
|
gptkbp:weight
|
gptkb:Integer
|
|
gptkbp:bfsParent
|
gptkb:Dedekind_eta_function
gptkb:Lambert_series
gptkb:Langlands_program
gptkb:Zeta_function
|
|
gptkbp:bfsLayer
|
5
|