On the polynomial Szemerédi theorem in finite fields
Abstract
Let $P_1,\dots,P_m\in\mathbb{Z}[y]$ be any linearly independent polynomials with zero constant term. We show that there exists a $\gamma>0$ such that any subset of $\mathbb{F}_q$ of size at least $q^{1\gamma}$ contains a nontrivial polynomial progression $x,x+P_1(y),\dots,x+P_m(y)$, provided the characteristic of $\mathbb{F}_q$ is large enough.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 DOI:
 10.48550/arXiv.1802.02200
 arXiv:
 arXiv:1802.02200
 Bibcode:
 2018arXiv180202200P
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Combinatorics
 EPrint:
 23 pages