On the torus, Hausdorff dimension above a threshold 1-epsilon forces arbitrary-length polynomial progressions for distinct-degree polynomials with zero constant terms.
Improved estimates for polynomial R oth type theorems in finite fields
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Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus
On the torus, Hausdorff dimension above a threshold 1-epsilon forces arbitrary-length polynomial progressions for distinct-degree polynomials with zero constant terms.