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gptkbp:instanceOf
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gptkb:mathematical_concept
gptkb:modular_group
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gptkbp:appearsIn
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elliptic functions
L-functions
modular forms theory
|
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gptkbp:definedIn
|
upper half-plane
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gptkbp:field
|
gptkb:mathematics
complex analysis
number theory
|
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gptkbp:firstDefined
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gptkb:Gotthold_Eisenstein
|
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gptkbp:generalizes
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gptkb:Hilbert_Eisenstein_series
gptkb:Maass_forms
gptkb:Siegel_Eisenstein_series
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gptkbp:hasApplication
|
partition function
zeta functions
automorphic representations
modular forms classification
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gptkbp:hasEquation
|
yes
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gptkbp:hasFourierExpansion
|
yes
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gptkbp:hasSpecialCase
|
classical Eisenstein series
|
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gptkbp:heldBy
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eigenfunction of Hecke operators
holomorphic for k > 2
non-cuspidal modular form
|
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gptkbp:namedAfter
|
gptkb:Gotthold_Eisenstein
|
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gptkbp:relatedTo
|
gptkb:modular_group
Fourier series
automorphic forms
|
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gptkbp:satisfies
|
modular invariance
|
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gptkbp:usedIn
|
gptkb:Langlands_program
representation theory
theory of modular forms
|
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gptkbp:weight
|
even integer k > 2
|
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gptkbp:bfsParent
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gptkb:Ferdinand_Eisenstein
gptkb:Gotthold_Eisenstein
|
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gptkbp:bfsLayer
|
5
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|
https://www.w3.org/2000/01/rdf-schema#label
|
Eisenstein series
|