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An improved bound in Wirsing's problem (1912.09013v1)
Published 19 Dec 2019 in math.NT
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.