On the Hausdorff Dimension of weighted exactly Approximable Vectors

Prasuna Bandi; Reynold Fregoli

On the Hausdorff Dimension of weighted exactly Approximable Vectors

Number Theory 2026-01-21 v1

Authors: Prasuna Bandi , Reynold Fregoli

Abstract

We show that the Hausdorff dimension of $\boldsymbol w$ -weighted $\tau$ -exactly approximable vectors in $\mathbb R^d$ coincides with the Hausdorff dimension of $\boldsymbol w$ -weighted $\tau$ -approximable vectors, generalizing a result of the first named author and De Saxc\'e.

Keywords

Hausdorff dimension weighted approximable vectors Diophantine approximation metric number theory

Cite

@article{arxiv.2601.12121,
  title  = {On the Hausdorff Dimension of weighted exactly Approximable Vectors},
  author = {Prasuna Bandi and Reynold Fregoli},
  journal= {arXiv preprint arXiv:2601.12121},
  year   = {2026}
}

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