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
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
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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}.
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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.