Narrow Progressions in the Primes

Terence Tao () and Tamar Ziegler ()
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Terence Tao: UCLA Department of Mathematics
Tamar Ziegler: The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram

A chapter in Analytic Number Theory, 2015, pp 357-379 from Springer

Abstract: Abstract In a previous paper of the authors, we showed that for any polynomials P 1 , … , P k ∈ ℤ [ m ] $$P_{1},\ldots,P_{k} \in \mathbb{Z}[\mathbf{m}]$$ with P 1 ( 0 ) = … = P k ( 0 ) $$P_{1}(0) =\ldots = P_{k}(0)$$ and any subset A of the primes in [N] = { 1, …, N} of relative density at least δ > 0, one can find a “polynomial progression” a + P 1 ( r ) , … , a + P k ( r ) $$a + P_{1}(r),\ldots,a + P_{k}(r)$$ in A with 0

Keywords: Polynomial Progressions; Dense Model Theorem; Gowers Norm; Clear Denominators; Arithmetic Progression (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22240-0_22

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DOI: 10.1007/978-3-319-22240-0_22

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