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arXiv · 1912.09013

An improved bound in Wirsing's problem

Dzmitry Badziahin·Johannes Schleischitz
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Abstract

We improve the lower bound for the classical exponent of approximation $w_{n}^{\ast}(\xi)$ connected to Wirsing's famous problem of approximation to real numbers by algebraic numbers of degree at most $n$. Our bound exceeds $n/\sqrt{3}\approx 0.5773n$ and thus provides a reasonable qualitative improvement to previous bounds of order $n/2+O(1)$. We further establish new relations between several classical exponents of approximation.

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Dzmitry Badziahin, Johannes Schleischitz. 2019-12-19. An improved bound in Wirsing's problem. https://arxiv.org/abs/1912.09013

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