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arXiv · 1806.05989

Über die Funktionen des Irrationalitätsmaßes für zwei irrationalen Zahlen

Nikolay G. Moshchevitin
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Abstract

For real $ξ$ we consider irrationality measure function $ψ_ξ(t) = \min_{1\le q \le t, \, q\in \mathbb{Z}} ||qξ||$. We prove that in the case $α\pm β\not\in \mathbb{Z}$ there exist arbitrary large values of $t$ with $|ψ_α(t) -ψ_β(t)| \ge\left(\sqrt{\frac{\sqrt{5}+1}{2}}-1\right) \min (ψ_α(t), ψ_β(t))$. This result is optimal.

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BibTeXRIS

Nikolay G. Moshchevitin. 2018-06-15. Über die Funktionen des Irrationalitätsmaßes für zwei irrationalen Zahlen. https://arxiv.org/abs/1806.05989

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