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gptkbp:instanceOf
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gptkb:automorphic_form
gptkb:mathematical_concept
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gptkbp:definedIn
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upper half-plane
|
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gptkbp:eigenfunctionOf
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hyperbolic Laplacian
|
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gptkbp:field
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gptkb:mathematics
modular forms
number theory
automorphic forms
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gptkbp:FourierCoefficients
|
arithmetic significance
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gptkbp:generalizes
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modular forms
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gptkbp:hasFourierExpansion
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yes
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gptkbp:hasInvariant
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modular group
congruence subgroups
|
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gptkbp:hasType
|
gptkb:cusp_form
gptkb:Eisenstein_series
non-cuspidal form
|
|
https://www.w3.org/2000/01/rdf-schema#label
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Maass forms
|
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gptkbp:introducedIn
|
1949
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gptkbp:namedAfter
|
gptkb:Hans_Maass
|
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gptkbp:relatedTo
|
gptkb:Selberg_trace_formula
gptkb:modular_curves
gptkb:Laplace-Beltrami_operator
gptkb:modular_group_PSL(2,_Z)
Hecke operators
modular forms
L-functions
spectral decomposition
automorphic Laplacian
automorphic spectrum
modular Laplacian
modular symbols
non-holomorphic Eisenstein series
non-holomorphic modular forms
quantum unique ergodicity
|
|
gptkbp:satisfies
|
modular invariance
growth condition at infinity
Laplace eigenfunction equation
|
|
gptkbp:studiedBy
|
gptkb:André_Weil
gptkb:Atle_Selberg
gptkb:Peter_Sarnak
gptkb:Dorian_Goldfeld
gptkb:Hans_Maass
|
|
gptkbp:studiedIn
|
representation theory
spectral theory
automorphic representations
|
|
gptkbp:usedIn
|
gptkb:Langlands_program
arithmetic geometry
quantum chaos
spectral theory of automorphic forms
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gptkbp:bfsParent
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gptkb:Eisenstein_series
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gptkbp:bfsLayer
|
5
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