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

• ##### Victor Beresnevich
Acta Arithmetica (Impact Factor: 0.47). 03/2008; DOI: 10.4064/aa117-1-4
Source: arXiv

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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