| dbo:abstract
|
- In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers.It is an important inequality in analytic number theory, named for I. M. Vinogradov. More specifically, let count the number of solutions to the system of simultaneous Diophantine equations in variables given by with . That is, it counts the number of equal sums of powers with equal numbers of terms and equal exponents,up to th powers and up to powers of . An alternative analytic expression for is where Vinogradov's mean-value theorem gives an upper bound on the value of . A strong estimate for is an important part of the Hardy-Littlewood method for attacking Waring's problem and also for demonstrating a zero free region for the Riemann zeta-function in the critical strip. Various bounds have been produced for , valid for different relative ranges of and . The classical form of the theorem applies when is very large in terms of . An analysis of the proofs of the Vinogradov mean-value conjecture can be found in the Bourbaki Séminaire talk by Lillian Pierce. (en)
|
| dbo:wikiPageID
| |
| dbo:wikiPageLength
|
- 7905 (xsd:nonNegativeInteger)
|
| dbo:wikiPageRevisionID
| |
| dbo:wikiPageWikiLink
| |
| dbp:wikiPageUsesTemplate
| |
| dcterms:subject
| |
| rdfs:comment
|
- In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers.It is an important inequality in analytic number theory, named for I. M. Vinogradov. More specifically, let count the number of solutions to the system of simultaneous Diophantine equations in variables given by with . That is, it counts the number of equal sums of powers with equal numbers of terms and equal exponents,up to th powers and up to powers of . An alternative analytic expression for is where Vinogradov's mean-value theorem gives an upper bound on the value of . (en)
|
| rdfs:label
|
- Vinogradov's mean-value theorem (en)
|
| owl:sameAs
| |
| prov:wasDerivedFrom
| |
| foaf:isPrimaryTopicOf
| |
| is dbo:wikiPageWikiLink
of | |
| is foaf:primaryTopic
of | |
