Monstrous Moonshine conjecture

E656687

The Monstrous Moonshine conjecture is a famous result in mathematics that reveals a deep and unexpected connection between the Monster finite simple group and modular functions in number theory.

All labels observed (5)

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Statements (48)

Predicate Object
instanceOf mathematical conjecture ⓘ
result in number theory ⓘ
alsoKnownAs Moonshine conjecture ⓘ
associatedWith Monster group ⓘ
largest sporadic simple group ⓘ
sporadic simple groups ⓘ
concerns relationship between Monster group representations and modular function coefficients ⓘ
unexpected connection between finite simple groups and modular functions ⓘ
connectedTo conformal field theory ⓘ
genus zero property of modular curves ⓘ
string theory ⓘ
coreIdea Fourier coefficients of the modular j-invariant are linearly related to sums of dimensions of Monster group representations ⓘ
field finite group theory ⓘ
group theory ⓘ
modular forms ⓘ
number theory ⓘ
representation theory ⓘ
vertex operator algebras ⓘ
formulatedInPublication Monstrous Moonshine (Conway–Norton paper) ⓘ
linked to: monstrous moonshine
formulatedInYear 1979 ⓘ
historicalNote name refers to the mysterious and surprising nature of the connection (moonshine) and the Monster group (monstrous) ⓘ
implies McKay–Thompson series are Hauptmoduln for genus zero groups ⓘ
existence of a graded infinite-dimensional Monster module ⓘ
inspired Mathieu moonshine ⓘ
umbral moonshine ⓘ
involves McKay–Thompson series ⓘ
graded representation of the Monster group ⓘ
modular functions for genus zero groups ⓘ
modular j-invariant ⓘ
vertex operator algebra structure ⓘ
keyObject Monster vertex operator algebra V^natural ⓘ
mathematicsSubjectClassification 11Fxx ⓘ
20C34 ⓘ
proofCompletedBy Borcherds proof of the Moonshine conjecture ⓘ
proofPublishedInYear 1992 ⓘ
provedBy Richard E. Borcherds ⓘ
recognizedBy Fields Medal for Richard Borcherds in 1998 ⓘ
relates Fourier coefficients of modular functions ⓘ
Monster group ⓘ
dimensions of irreducible representations of the Monster group ⓘ
modular forms of weight 0 ⓘ
modular functions ⓘ
statedBy John H. Conway ⓘ
Simon P. Norton ⓘ
status proved ⓘ
usesInProof automorphic forms ⓘ
generalized Kac–Moody algebras ⓘ
vertex operator algebras ⓘ

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Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Simon P. Norton → knownFor → Monstrous Moonshine conjecture ⓘ
Conway–Norton collaboration → resultedIn → Conway–Norton conjectures on monstrous moonshine ⓘ
linked to: Monstrous Moonshine conjecture
M → isCentralObjectIn → monstrous moonshine conjectures ⓘ
linked to: Monstrous Moonshine conjecture
Monstrous Moonshine conjecture → implies → McKay–Thompson series are Hauptmoduln for genus zero groups ⓘ
linked to: Monstrous Moonshine conjecture
Monstrous Moonshine conjecture → alsoKnownAs → Moonshine conjecture ⓘ
linked to: Monstrous Moonshine conjecture