Über die Funktionen des Irrationalitätsmaßes

Nikolay G. Moshchevitin

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arXiv · 1611.07183

Über die Funktionen des Irrationalitätsmaßes

Nikolay G. Moshchevitin

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Abstract

We study two irrationality measure functions $ψ_α^{[2]} (t) $ and $ψ_α^{[2]*} (t)$ related to the "second best" approximations to a real numbers and prove some results on the structure of the corresponding Diophantine spectra. It happened that the first two elements of the spectrum for the function $ψ_α^{[2]*} (t)$ are associated with the numbers $\frac{1+\sqrt{5}}{2}$ and $e =\sum_{n=0}^\infty \frac{1}{n!}$.

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Nikolay G. Moshchevitin. 2016-11-22. Über die Funktionen des Irrationalitätsmaßes. https://arxiv.org/abs/1611.07183

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