TY - JOUR
T1 - Three-term polynomial progressions in subsets of finite fields
AU - Peluse, Sarah
N1 - 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).
UR - https://www.scopus.com/pages/publications/85051673829
UR - https://www.scopus.com/inward/citedby.url?scp=85051673829&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1768-z
DO - 10.1007/s11856-018-1768-z
M3 - Article
AN - SCOPUS:85051673829
SN - 0021-2172
VL - 228
SP - 379
EP - 405
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -