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MULTIDIMENSIONAL VAN DER CORPUT SETS AND SMALL FRACTIONAL PARTS OF POLYNOMIALS
Published online by Cambridge University Press: 07 January 2019
Abstract
We establish Diophantine inequalities for the fractional parts of generalized polynomials, in particular for sequences $\unicode[STIX]{x1D708}(n)=\lfloor n^{c}\rfloor +n^{k}$ with
$c>1$ a non-integral real number and
$k\in \mathbb{N}$, as well as for
$\unicode[STIX]{x1D708}(p)$ where
$p$ runs through all prime numbers. This is related to classical work of Heilbronn and to recent results of Bergelson et al.
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- Copyright © University College London 2019
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