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Preprint Number 1380

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1380. Sarah Peluse
On the polynomial Szemerédi's theorem in finite fields

Submission date: 6 February 2018


Let P_1, ... ,P_m in Z[y] be any linearly independent polynomials with zero constant term. We show that there exists a γ >0 such that any subset of F_q of size at least q^{1-γ} contains a nontrivial polynomial progression x,x+P_1(y), ... , x+P_m(y), provided the characteristic of F_q is large enough.

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Full text arXiv 1802.02200: pdf, ps.

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