## Abstract

Let P _{1} ; . . . ; P _{m} ∈ Z[y] be any linearly independent polynomials with zero constant term. We show that there exists 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 that the characteristic of F _{q} is large enough.

Original language | English (US) |
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Pages (from-to) | 749-774 |

Number of pages | 26 |

Journal | Duke Mathematical Journal |

Volume | 168 |

Issue number | 5 |

DOIs | |

State | Published - Apr 1 2019 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)