The Gaussian primes contain arbitrarily shaped constellations

2006/12/01 by Terence Tao · 4 citations
Mathematics · #Advanced Topology and Set Theory #Algorithm #Analytic Number Theory Research #Combinatorics #Computer science #Discrete mathematics #Gaussian #Gaussian integer #Generalization #Hypergraph #Lemma (botany) #Limits and Structures in Graph Theory #Mathematical analysis #Mathematics #Measure (data warehouse) #Physics #Pseudorandom number generator

paper · doi:10.1007/bf02789444

crossref issued 2006/12/01 · crossref published 2006/12/01 · crossref published-print 2006/12/01 · openalex publication_date 2006/12/01 · crossref created 2008/12/10 · crossref deposited 2019/05/20 · openalex created_date 2025/10/10 · crossref indexed 2026/03/07 · openalex updated_date 2026/07/29

Citations

• On sets of integers containing k elements in arithmetic progression
• Higher correlations of divisor sums related to primes III: k-correlations
• Regularity Lemma for k‐uniform hypergraphs
• A variant of the hypergraph removal lemma
• Extremal problems on set systems
• The primes contain arbitrarily long arithmetic progressions
• Hypergraph regularity and the multidimensional Szemerédi theorem
• A new proof of Szemerédi's theorem
• A quantitative ergodic theory proof of Szemerédi's theorem

Cited by

• A multi-dimensional Szemerédi theorem for the primes via a correspondence principle
• A Multidimensional Szemerédi Theorem in the Primes via Combinatorics
• Constellations in Pd
• Obstructions to Uniformity and Arithmetic Patterns in the Primes
• Green–Tao theorem [wikipedia]