Roth's 3-term arithmetic progression theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Roth's_theorem
|
| gptkbp:field |
number theory
additive combinatorics |
| gptkbp:generalizes |
Van der Waerden's theorem
|
| gptkbp:hasSpecialCase |
gptkb:Szemerédi's_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Roth's 3-term arithmetic progression theorem
|
| gptkbp:implies |
no large subset of integers avoids 3-term arithmetic progressions
|
| gptkbp:mainFunction |
Fourier analysis
|
| gptkbp:namedAfter |
gptkb:Klaus_Roth
|
| gptkbp:provenBy |
gptkb:Klaus_Roth
|
| gptkbp:publishedIn |
gptkb:Mathematika
|
| gptkbp:relatedTo |
gptkb:Erdős–Turán_conjecture
Behrend's construction |
| gptkbp:sentence |
Any subset of the integers from 1 to N with positive density contains a nontrivial 3-term arithmetic progression for sufficiently large N.
|
| gptkbp:yearProved |
1953
|
| gptkbp:bfsParent |
gptkb:Roth's_Theorem
|
| gptkbp:bfsLayer |
8
|