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 (2)
| Label | Occurrences |
|---|---|
| Conway–Norton conjectures on monstrous moonshine | 1 |
| Monstrous Moonshine conjecture canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338528 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Monstrous Moonshine conjecture Context triple: [Simon P. Norton, knownFor, Monstrous Moonshine conjecture]
-
A.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
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B.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
-
C.
Ramanujan partition congruences
Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
-
D.
Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
-
E.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Monstrous Moonshine conjecture Target entity description: 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.
-
A.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
-
B.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
-
C.
Ramanujan partition congruences
Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
-
D.
Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
-
E.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Monstrous Moonshine conjecture Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Conway–Norton conjectures on monstrous moonshine