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Moment transference principles and multiplicative diophantine approximation on hypersurfaces

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arxiv 2408.10911 v2 pith:FY6Z37QW submitted 2024-08-20 math.NT

Sam Chow , Han Yu This is my paper · ORCID
classification math.NT
keywords approximationdatamomentmultiplicativeprinciplestransferenceaccordingaddress
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We determine the generic multiplicative approximation rate on a hypersurface. There are four regimes, according to convergence or divergence and curved or flat, and we address all of them. Using geometry and arithmetic in Fourier space, we develop a general framework of moment transference principles, which convert Lebesgue data into data for some other measure.

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  1. Simultaneous and multiplicative Diophantine approximation on missing-digit fractals

    math.NT 2024-12 conditional novelty 7.0 of 10

    Measures with large Fourier l1 dimension satisfy Khinchin-type and Gallagher-type Diophantine laws, giving new approximation and counting results on missing-digit fractals.

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