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- W2051194735 abstract "Abstract In this paper, the Khintchine-type theorems of Beresnevich ( Acta Arith . 90 (1999), 97) and Bernik ( Acta Arith . 53 (1989), 17) for polynomials are generalised to incorporate a natural restriction on derivatives. This represents the first attempt to solve a problem posed by Bernik, Kleinbock and Margulis ( Int. Math. Res. Notices 2001 (9) (2001), 453). More specifically, the main result provides a probabilistic criterion for the solvability of the system of inequalities | P ( x )| < Ψ 1 ( H ) and | P ′( x )| < Ψ 2 ( H ) in integral polynomials P of degree ≤ n and height H , where Ψ 1 and Ψ 2 are fairly general error functions. The proof builds upon Sprindzuk's method of essential and inessential domains and the recent ideas of Beresnevich, Bernik and Götze ( Compositio Math . 146 (2010), 1165) concerning the distribution of algebraic numbers." @default.
- W2051194735 created "2016-06-24" @default.
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- W2051194735 date "2011-08-01" @default.
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- W2051194735 title "ON A PROBLEM OF BERNIK, KLEINBOCK AND MARGULIS" @default.
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- W2051194735 doi "https://doi.org/10.1017/s0017089511000255" @default.
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