publication . Article . Preprint . 2009

Green–Tao theorem in function fields

Le, Thai Hoang;
Open Access
  • Published: 18 Aug 2009 Journal: Acta Arithmetica, volume 147, pages 129-152 (issn: 0065-1036, eissn: 1730-6264, Copyright policy)
  • Publisher: Institute of Mathematics, Polish Academy of Sciences
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\mathbf{F}_q[t]$ contain configurations of the form $\{f+ Pg : \d(P)<k \}, g \neq 0$.
free text keywords: Algebra and Number Theory, Algebra, Green–Tao theorem, Mathematics, Mathematics - Number Theory, Mathematics - Combinatorics
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publication . Article . Preprint . 2009

Green–Tao theorem in function fields

Le, Thai Hoang;