Dense subsets of [N]^n contain configurations x, x + r^{m1}e1, ..., x + r^{mn}en for any fixed n and increasing exponents m_i, with density threshold (log N)^{-c}.
F., Sisask, O., An improvement to the Kelley–Meka bounds on three-term arithmetic progressions, preprint
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
verdicts
UNVERDICTED 4representative citing papers
The paper establishes the existence of positive constants c and c_IP for the IP Szemeredi theorem over finite fields and gives strong quantitative bounds in the special cases of Roth and IP-Roth theorems.
Characterizes the range of c where linear equations with s variables are partition regular over floor(n^c), gives density bounds, and updates a Fourier-analytic transference principle.
f(n²,n) ≥ n + (1/√2 + o(1))√n and f(p²,p) ≤ 2p − (√(2/3) − o(1))√(p/log p) for large primes p.
citing papers explorer
-
A multidimensional Szemer\'{e}di theorem in integers
Dense subsets of [N]^n contain configurations x, x + r^{m1}e1, ..., x + r^{mn}en for any fixed n and increasing exponents m_i, with density threshold (log N)^{-c}.
-
On the Furstenberg-Katznelson constant for the IP Szemeredi theorem over finite fields
The paper establishes the existence of positive constants c and c_IP for the IP Szemeredi theorem over finite fields and gives strong quantitative bounds in the special cases of Roth and IP-Roth theorems.
-
Additive Ramsey theory over Piatetski-Shapiro numbers
Characterizes the range of c where linear equations with s variables are partition regular over floor(n^c), gives density bounds, and updates a Fourier-analytic transference principle.
-
Hitting Arithmetic Progressions at the Square-Root Scale
f(n²,n) ≥ n + (1/√2 + o(1))√n and f(p²,p) ≤ 2p − (√(2/3) − o(1))√(p/log p) for large primes p.