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· arXiv 2602.05593

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math.CA 1

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Fourier analytic variants of the Furstenberg and Kakeya problems

math.CA · 2026-05-20 · unverdicted · novelty 7.0

The authors prove that the Fourier dimension Δ(s,t) of any (s,t)-Kakeya set in the plane satisfies 2st/(s+2t) ≤ Δ(s,t) ≤ min{s,2t} for 0<s,t<1, with analogous bounds in the Furstenberg and Fourier-direction variants.

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  • Fourier analytic variants of the Furstenberg and Kakeya problems math.CA · 2026-05-20 · unverdicted · none · ref 1

    The authors prove that the Fourier dimension Δ(s,t) of any (s,t)-Kakeya set in the plane satisfies 2st/(s+2t) ≤ Δ(s,t) ≤ min{s,2t} for 0<s,t<1, with analogous bounds in the Furstenberg and Fourier-direction variants.