Turán–Kubilius inequality
E750083
The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical inequality
ⓘ
result in probabilistic number theory ⓘ |
| appearsIn |
research on additive functions
ⓘ
texts on probabilistic number theory ⓘ |
| appliesTo |
additive arithmetic function
ⓘ
strongly additive arithmetic function ⓘ |
| assumption | additivity of the arithmetic function ⓘ |
| compares | values of an additive function to its expected value ⓘ |
| context |
metric number theory
ⓘ
probabilistic methods in number theory ⓘ |
| field |
number theory
ⓘ
probabilistic number theory ⓘ |
| hasConsequence | almost all integers have typical additive-function behavior ⓘ |
| historicalPeriod | 20th-century mathematics ⓘ |
| implies | concentration of additive functions around their mean ⓘ |
| mathematicalArea |
analytic number theory
ⓘ
probability theory on arithmetic functions ⓘ |
| namedAfter |
J. Kubilius
NERFINISHED
ⓘ
Pál Turán NERFINISHED ⓘ |
| provides | bounds on the distribution of additive arithmetic functions ⓘ |
| relatedTo |
Erdős–Kac theorem
NERFINISHED
ⓘ
distribution of prime factors ⓘ normal order of arithmetic functions ⓘ |
| relatesConcept |
distribution of additive functions over integers
ⓘ
mean value of an additive function ⓘ variance of an additive function ⓘ |
| subjectOf | additive arithmetic functions ⓘ |
| typeOfBound | mean-square bound ⓘ |
| typicalDomain | positive integers ⓘ |
| usedFor |
estimating variance of additive arithmetic functions
ⓘ
proving normal order results for arithmetic functions ⓘ studying distribution of values of additive functions ⓘ |
| usedIn |
analysis of additive functions like log n
ⓘ
analysis of additive functions like Ω(n) ⓘ analysis of additive functions like ω(n) ⓘ |
Referenced by (2)
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