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<p>In this paper, we obtain a zero-infinity law for the <i>s</i>-dimensional Hausdorff measure of set of exact approximation order by rational numbers, which provides a partial answer to that question posed by Bugeaud (Math Ann 327(2):171–190, 2003). We also calculate the Hausdorff dimension of the set of exactly approximable planar vectors in the simultaneous case.</p>

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Metric results in exact diophantine approximation

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Bo Tan,
  • Chen Tian,
  • Qing-Long Zhou

摘要

In this paper, we obtain a zero-infinity law for the s-dimensional Hausdorff measure of set of exact approximation order by rational numbers, which provides a partial answer to that question posed by Bugeaud (Math Ann 327(2):171–190, 2003). We also calculate the Hausdorff dimension of the set of exactly approximable planar vectors in the simultaneous case.