Sets of Exact Approximation Order by Complex rational numbers

Yubin He; Ying Xiong

doi:10.1007/s00209-021-02906-4

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arXiv · 2105.01917

Sets of Exact Approximation Order by Complex rational numbers

Yubin He·Ying Xiong

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Abstract

For a nonincreasing function $ψ$, let $\textrm{Exact}(ψ)$ be the set of complex numbers that are approximable by complex rational numbers to order $ψ$ but to no better order. In this paper, we obtain the Hausdorff dimension and packing dimension of $\textrm{Exact}(ψ)$ when $ψ(x)=o(x^{-2})$. We also prove that the lower bound of the Hausdorff dimension is greater than $2-τ/(1-2τ)$ when $τ=\limsup_{x\to\infty}ψ(x)x^2$ small enough.

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BibTeX RIS

Yubin He, Ying Xiong. 2021-05-19. Sets of Exact Approximation Order by Complex rational numbers. https://doi.org/10.1007/s00209-021-02906-4

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