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- W4385373208 abstract "Let $varepsilon>0$. We construct an explicit, full-measure set of $alpha in[0,1]$ such that if $gamma in mathbb{R}$ then, for almost all $beta in[0,1]$, if $delta in mathbb{R}$ then there are infinitely many integers $ngeq 1$ for which [ n Vert nalpha - gamma Vert cdot Vert nbeta - delta Vert < frac{(log log n)^{3 + varepsilon}}{log n}. ] This is a significant quantitative improvement over a result of the first author and Zafeiropoulos. We show, moreover, that the exceptional set of $beta$ has Fourier dimension zero, alongside further applications to badly approximable numbers and to lacunary diophantine approximation. Our method relies on a dispersion estimate and the Three Distance Theorem." @default.
- W4385373208 created "2023-07-29" @default.
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- W4385373208 date "2023-07-27" @default.
- W4385373208 modified "2023-10-18" @default.
- W4385373208 title "Dispersion and Littlewood's conjecture" @default.
- W4385373208 doi "https://doi.org/10.48550/arxiv.2307.14871" @default.
- W4385373208 hasPublicationYear "2023" @default.
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