TY - JOUR
T1 - Three-term polynomial progressions in subsets of finite fields
AU - Peluse, Sarah
N1 - Funding Information: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute during the Spring 2017 semester. The author is also supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-114747 and by the Stanford University Mayfield Graduate Fellowship. Publisher Copyright: © 2018, Hebrew University of Jerusalem.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - Bourgain and Chang recently showed that any subset of Fp of density ≫p−1/15 contains a nontrivial progression x, x + y, x + y2. We answer a question of theirs by proving that if P1, P2 ∈ ℤ[y] are linearly independent and satisfy P1(0) = P2(0) = 0, then any subset of Fp of density ≫P1,P2p−1/24 contains a nontrivial polynomial progression x, x + P1(y), x + P2(y).
AB - Bourgain and Chang recently showed that any subset of Fp of density ≫p−1/15 contains a nontrivial progression x, x + y, x + y2. We answer a question of theirs by proving that if P1, P2 ∈ ℤ[y] are linearly independent and satisfy P1(0) = P2(0) = 0, then any subset of Fp of density ≫P1,P2p−1/24 contains a nontrivial polynomial progression x, x + P1(y), x + P2(y).
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U2 - https://doi.org/10.1007/s11856-018-1768-z
DO - https://doi.org/10.1007/s11856-018-1768-z
M3 - Article
SN - 0021-2172
VL - 228
SP - 379
EP - 405
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -