A Multidimensional Szemerédi Theorem in the Primes via Combinatorics

2018/11/30 by Brian Cook, Ákos Magyar, Tatchai Titichetrakun · 2 citations
Engineering · Mathematics · #Affine transformation #Analytic Number Theory Research #Arithmetic progression #Combinatorics #Discrete mathematics #Extension (predicate logic) #Extremal combinatorics #Limits and Structures in Graph Theory #Mathematics #Pure mathematics #Tuple #graph theory and CDMA systems

paper · doi:10.1007/s00026-018-0402-4

crossref issued 2018/11/30 · crossref published 2018/11/30 · crossref published-online 2018/11/30 · openalex publication_date 2018/11/30 · crossref created 2018/11/30 · crossref published-print 2018/12/01 · openalex created_date 2018/12/11 · crossref deposited 2019/11/29 · crossref indexed 2026/06/18 · openalex updated_date 2026/08/05

Citations

• On sets of integers containing k elements in arithmetic progression
• Higher correlations of divisor sums related to primes III: k-correlations
• Szemer'edi's regularity lemma revisited
• The Gaussian primes contain arbitrarily shaped constellations
• A multi-dimensional Szemerédi theorem for the primes via a correspondence principle
• A variant of the hypergraph removal lemma
• The primes contain arbitrarily long arithmetic progressions
• Hypergraph regularity and the multidimensional Szemerédi theorem
• The counting lemma for regulark‐uniform hypergraphs

Cited by

• Polynomial configurations in dense subsets of the prime lattice
• Green–Tao theorem [wikipedia]