TY - JOUR
T1 - On the polynomial szemerédi theorem in finite fields
AU - Peluse, Sarah
N1 - Funding Information:
The author’s work was partially supported by National Science Foundation Graduate Research Fellowship Program Grant DGE-114747 and by the Stanford University Mayfield Graduate Fellowship.
Funding Information:
The author thanks Ben Green, Kannan Soundararajan, Julia Wolf, and the anonymous referees for helpful comments on earlier versions of this paper. The author's work was partially supported by National Science Foundation Graduate Research Fellowship Program Grant DGE-114747 and by the Stanford University Mayfield Graduate Fellowship
Publisher Copyright:
© 2019.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-2018-0051
DO - 10.1215/00127094-2018-0051
M3 - Article
AN - SCOPUS:85063616733
SN - 0012-7094
VL - 168
SP - 749
EP - 774
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 5
ER -