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- Title
A Multidimensional Szemerédi Theorem in the Primes via Combinatorics.
- Authors
Cook, Brian; Magyar, Ákos; Titichetrakun, Tatchai
- Abstract
Let A be a subset of positive relative upper density of Pd, the d-tuples of primes. We present an essentially self-contained, combinatorial argument to show that A contains infinitely many affine copies of any finite set F⊆Zd. This provides a natural multidimensional extension of the theorem of Green and Tao on the existence of long arithmetic progressions in the primes.
- Subjects
PRIME numbers; COMBINATORICS; FINITE fields; EXISTENCE theorems
- Publication
Annals of Combinatorics, 2018, Vol 22, Issue 4, p711
- ISSN
0218-0006
- Publication type
Article
- DOI
10.1007/s00026-018-0402-4