Roth's theorem

GPTKB entity

Statements (17)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:alsoKnownAs gptkb:Roth's_theorem_on_arithmetic_progressions
gptkbp:field number theory
gptkbp:generalizes gptkb:van_der_Waerden's_theorem
https://www.w3.org/2000/01/rdf-schema#label Roth's theorem
gptkbp:implies no large subset of integers is free of three-term arithmetic progressions
gptkbp:influenced additive combinatorics
the study of arithmetic progressions in sets of integers
gptkbp:namedAfter gptkb:Klaus_Roth
gptkbp:provenBy Fourier analysis
gptkbp:publishedIn gptkb:Proceedings_of_the_London_Mathematical_Society
gptkbp:relatedTo gptkb:Szemerédi's_theorem
gptkbp:state Any subset of the integers from 1 to N with positive density contains a nontrivial three-term arithmetic progression for sufficiently large N.
gptkbp:yearProved 1953
gptkbp:bfsParent gptkb:Diophantine_approximation
gptkb:Klaus_Roth
gptkbp:bfsLayer 6