Monstrous Moonshine conjecture

E656687

mathematical conjecture result in number theory

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.

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Observed surface forms (1)

Surface form	Occurrences
Conway–Norton conjectures on monstrous moonshine	1

Statements (48)

Predicate	Object
instanceOf	mathematical conjecture ⓘ result in number theory ⓘ
alsoKnownAs	Moonshine conjecture NERFINISHED ⓘ
associatedWith	Monster group NERFINISHED ⓘ 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) NERFINISHED ⓘ
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 NERFINISHED ⓘ existence of a graded infinite-dimensional Monster module ⓘ
inspired	Mathieu moonshine NERFINISHED ⓘ umbral moonshine NERFINISHED ⓘ
involves	McKay–Thompson series NERFINISHED ⓘ graded representation of the Monster group ⓘ modular functions for genus zero groups ⓘ modular j-invariant NERFINISHED ⓘ vertex operator algebra structure ⓘ
keyObject	Monster vertex operator algebra V^natural NERFINISHED ⓘ
mathematicsSubjectClassification	11Fxx ⓘ 20C34 ⓘ
proofCompletedBy	Borcherds proof of the Moonshine conjecture ⓘ
proofPublishedInYear	1992 ⓘ
provedBy	Richard E. Borcherds NERFINISHED ⓘ
recognizedBy	Fields Medal for Richard Borcherds in 1998 ⓘ
relates	Fourier coefficients of modular functions ⓘ Monster group NERFINISHED ⓘ dimensions of irreducible representations of the Monster group ⓘ modular forms of weight 0 ⓘ modular functions ⓘ
statedBy	John H. Conway NERFINISHED ⓘ Simon P. Norton NERFINISHED ⓘ
status	proved ⓘ
usesInProof	automorphic forms ⓘ generalized Kac–Moody algebras NERFINISHED ⓘ vertex operator algebras ⓘ

Referenced by (2)

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 → Monstrous Moonshine conjecture ⓘ

this entity surface form: Conway–Norton conjectures on monstrous moonshine