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

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

2008-02-13

arxiv.org/abs/0802.1910v1

Acta Arith. 117 (2005), no. 1, 71-80

Mathematics

Number Theory

11 pages

Scientific paper

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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