Erdős–Wintner theorem
E637299
The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Erdős–Wintner theorem canonical | 3 |
| Delange theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7030753 — 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: Erdős–Wintner theorem Context triple: [Multiplicative Number Theory, hasClassicResult, Erdős–Wintner theorem]
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A.
Erdős–Kac theorem
The Erdős–Kac theorem is a fundamental result in probabilistic number theory stating that the number of distinct prime factors of a typical integer behaves like a normally distributed random variable.
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B.
Dirichlet's theorem on arithmetic progressions
Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
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C.
Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
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D.
Bateman–Horn conjecture
The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
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E.
Mertens’ theorems
Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
- 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: Erdős–Wintner theorem Target entity description: The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
-
A.
Erdős–Kac theorem
The Erdős–Kac theorem is a fundamental result in probabilistic number theory stating that the number of distinct prime factors of a typical integer behaves like a normally distributed random variable.
-
B.
Dirichlet's theorem on arithmetic progressions
Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
-
C.
Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
-
D.
Bateman–Horn conjecture
The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
-
E.
Mertens’ theorems
Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
- F. None of above. chosen
Statements (29)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in probabilistic number theory ⓘ |
| appliesTo | additive functions on positive integers ⓘ |
| assumes | additive arithmetic function ⓘ |
| characterizes | conditions for existence of limiting distribution of an additive arithmetic function ⓘ |
| codomain | real numbers ⓘ |
| concerns |
additive arithmetic functions
ⓘ
distribution of additive functions on integers ⓘ limiting distributions of arithmetic functions ⓘ |
| field |
number theory
ⓘ
probabilistic number theory ⓘ |
| hasConsequence | criteria for convergence in distribution of additive functions ⓘ |
| hasDomain | set of natural numbers ⓘ |
| hasProperty | gives necessary and sufficient conditions for limiting distribution of additive functions ⓘ |
| hasType | limit theorem ⓘ |
| historicalPeriod | 20th century mathematics ⓘ |
| implies | existence of a limiting distribution under certain summability conditions on the additive function ⓘ |
| influenced | development of probabilistic number theory ⓘ |
| namedAfter |
Aurel Wintner
ⓘ
Paul Erdős ⓘ
linked to:
Pál Erdős
|
| relatedTo |
Erdős–Kac theorem
ⓘ
additive functions ⓘ distribution of values of arithmetic functions ⓘ multiplicative functions ⓘ |
| usedIn |
analytic number theory
ⓘ
probabilistic methods in number theory ⓘ |
| usesConcept |
convergence in distribution
ⓘ
independence heuristics for prime factors ⓘ probability distribution ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Erdős–Wintner theorem Description of subject: The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Erdős–Wintner theorem