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arXiv · 0802.1910

On a theorem of V. Bernik in the metrical theory of Diophantine approximation

Victor Beresnevich
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Abstract

This paper goes back to a famous problem of Mahler in metrical Diophantine approximation. The problem has been settled by Sprindzuk and subsequently improved by Alan Baker and Vasili Bernik. In particular, Bernik's result establishes a convergence Khintchine type theorem for Diophantine approximation by polynomials, that is it allows arbitrary monotonic error of approximation. In the present paper the monotonicity assumption is completely removed.

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Victor Beresnevich. 2008-02-13. On a theorem of V. Bernik in the metrical theory of Diophantine approximation. https://arxiv.org/abs/0802.1910

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