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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:Langlands_program
gptkb:Theory_of_elliptic_curves
Modularity theorem
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gptkbp:definedIn
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A modular form that vanishes at all cusps
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gptkbp:example
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gptkb:Delta_function_(Ramanujan's_tau_function)
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gptkbp:field
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gptkb:Mathematics
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gptkbp:generalizes
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gptkb:Automorphic_cusp_forms
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gptkbp:hasSubfield
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gptkb:Number_theory
gptkb:Automorphic_forms
gptkb:Modular_forms
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https://www.w3.org/2000/01/rdf-schema#label
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Cusp forms
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gptkbp:notation
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S_k(Γ)
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gptkbp:property
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Finite dimension for fixed weight and level
Holomorphic on the upper half-plane
Rapid decay at cusps
Vector space over complex numbers
Fourier expansion at infinity has zero constant term
Orthogonal to Eisenstein series under Petersson inner product
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gptkbp:relatedTo
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gptkb:Eisenstein_series
Hecke operators
L-functions
Modular forms of weight k
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gptkbp:studiedBy
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gptkb:Atle_Selberg
gptkb:Erich_Hecke
gptkb:Goro_Shimura
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gptkbp:bfsParent
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gptkb:Automorphic_forms
gptkb:Modular_forms
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gptkbp:bfsLayer
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6
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