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.
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
NERFINISHED
ⓘ
Paul Erdős NERFINISHED ⓘ |
| relatedTo |
Erdős–Kac theorem
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.