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gptkbp:instanceOf
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gptkb:modular_function
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gptkbp:alsoKnownAs
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gptkb:j-invariant
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gptkbp:definedIn
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upper half-plane
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gptkbp:field
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gptkb:mathematics
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gptkbp:FourierExpansion
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j(z) = q^{-1} + 744 + 196884q + 21493760q^2 + ...
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gptkbp:hasApplication
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gptkb:algebraic_geometry
modular forms
theory of modular curves
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gptkbp:hasFourierExpansion
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true
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gptkbp:hasInvariant
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gptkb:modular_group_SL(2,Z)
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gptkbp:hasPoleAt
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infinity
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gptkbp:hasSubfield
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complex analysis
modular forms
number theory
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gptkbp:isAlgebraicInteger
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at CM points
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gptkbp:isGeneratorOf
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field of modular functions for SL(2,Z)
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gptkbp:isHauptmodulFor
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gptkb:modular_group_SL(2,Z)
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gptkbp:isHolomorphic
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true
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gptkbp:isMeromorphic
|
true
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gptkbp:isRationalFunctionOf
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modular lambda function
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gptkbp:isSurjectiveOnto
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gptkb:complex_plane
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gptkbp:mapType
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complex numbers
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gptkbp:namedAfter
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gptkb:Carl_Gustav_Jacobi
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gptkbp:q
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e^{2πiz}
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gptkbp:usedIn
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gptkb:monstrous_moonshine
class field theory
complex multiplication
elliptic curves
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https://www.w3.org/2000/01/rdf-schema#label
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modular function j(z)
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