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gptkbp:instanceOf
|
modular function
|
|
gptkbp:alsoKnownAs
|
gptkb:j-invariant
|
|
gptkbp:definedIn
|
upper half-plane
|
|
gptkbp:field
|
gptkb:mathematics
|
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gptkbp:FourierExpansion
|
j(z) = q^{-1} + 744 + 196884q + 21493760q^2 + ...
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gptkbp:hasApplication
|
gptkb:algebraic_geometry
modular forms
theory of modular curves
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|
gptkbp:hasFourierExpansion
|
true
|
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gptkbp:hasInvariant
|
gptkb:modular_group_SL(2,Z)
|
|
gptkbp:hasPoleAt
|
infinity
|
|
gptkbp:hasSubfield
|
complex analysis
modular forms
number theory
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
modular function j(z)
|
|
gptkbp:isAlgebraicInteger
|
at CM points
|
|
gptkbp:isGeneratorOf
|
field of modular functions for SL(2,Z)
|
|
gptkbp:isHauptmodulFor
|
gptkb:modular_group_SL(2,Z)
|
|
gptkbp:isHolomorphic
|
true
|
|
gptkbp:isMeromorphic
|
true
|
|
gptkbp:isRationalFunctionOf
|
modular lambda function
|
|
gptkbp:isSurjectiveOnto
|
gptkb:complex_plane
|
|
gptkbp:mapType
|
complex numbers
|
|
gptkbp:namedAfter
|
gptkb:Carl_Gustav_Jacobi
|
|
gptkbp:q
|
e^{2πiz}
|
|
gptkbp:usedIn
|
gptkb:monstrous_moonshine
class field theory
complex multiplication
elliptic curves
|
|
gptkbp:bfsParent
|
gptkb:Creature
|
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gptkbp:bfsLayer
|
5
|