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arXiv · 1606.03049

Multidimensional van der Corput sets and small fractional parts of polynomials

Manfred G. Madritsch·Robert F. Tichy
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Abstract

We establish Diophantine inequalities for the fractional parts of generalized polynomials $f$, in particular for sequences $\nu(n)=\lfloor n^c\rfloor+n^k$ with $c>1$ a non-integral real number and $k\in\mathbb{N}$, as well as for $\nu(p)$ where $p$ runs through all prime numbers. This is related to classical work of Heilbronn and to recent results of Bergelson \textit{et al.}

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BibTeXRIS

Manfred G. Madritsch, Robert F. Tichy. 2016-06-09. Multidimensional van der Corput sets and small fractional parts of polynomials. https://doi.org/10.1112/s0025579318000529

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