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- W2941993048 abstract "Let $Esubset mathbb{R}$ be a closed set of Hausdorff dimension $alphain (0, 1)$. Let $P: mathbb{R}to mathbb{R}$ be a polynomial without a constant term whose degree is bigger than one. We prove that if $E$ supports a probability measure satisfying certain dimension condition and Fourier decay condition, then $E$ contains three points $x, x+t, x+P(t)$ for some $t>0$. Our result extends the one of Laba and the third author to the polynomial setting, under the same assumption. It also gives an affirmative answer to a question in Henriot, Laba and the third author." @default.
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- W2941993048 date "2019-04-25" @default.
- W2941993048 modified "2023-10-11" @default.
- W2941993048 title "Polynomial Roth theorems on sets of fractional dimensions" @default.
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