On arithmetic structures in dense sets of integers

DOI10.1215/S0012-7094-02-11422-7zbMath1020.11010OpenAlexW1967102966MaRDI QIDQ1847946

Ben Green

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-02-11422-7

zbMATH Keywords

arithmetic progressionSzemerédi theoremSelberg sievesum of two squaresSárközy theoremsquare difference

Mathematics Subject Classification ID

Applications of sieve methods (11N36) Ramsey theory (05D10) Arithmetic progressions (11B25)

Related Items

Polynomial configurations in subsets of random and pseudo-random sets ⋮ Popular progression differences in vector spaces II ⋮ Arithmetic progressions with a pseudorandom step ⋮ ON A DIAGONAL QUADRIC IN DENSE VARIABLES ⋮ Multivariate Polynomial Values in Difference Sets ⋮ A maximal extension of the best-known bounds for the Furstenberg–Sárközy theorem ⋮ Binary Quadratic Forms in Difference Sets ⋮ John-type theorems for generalized arithmetic progressions and iterated sumsets ⋮ Structure Along Arithmetic Patterns in Sequences of Vectors ⋮ Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case ⋮ Difference sets and shifted primes ⋮ A general nonlinear version of Roth's theorem on the real line ⋮ Counting configuration-free sets in groups ⋮ Rado's criterion over squares and higher powers ⋮ Polynomial configurations in difference sets ⋮ The primes contain arbitrarily long polynomial progressions ⋮ A new proof of Sárközy’s theorem ⋮ Asymptotics for some polynomial patterns in the primes ⋮ Generations of correlation averages ⋮ Problems and Results on Intersective Sets ⋮ A multi-dimensional Szemerédi theorem for the primes via a correspondence principle

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