On small fractional parts of perturbed polynomials

Paolo Minelli

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arXiv · 2110.04167

On small fractional parts of perturbed polynomials

Paolo Minelli

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Abstract

Questions concerning small fractional parts of polynomials and pseudo-polynomials have a long history in analytic number theory. In this paper, we improve on earlier work by Madritsch and Tichy. In particular, let $f=P+\phi$ where $P$ is a polynomial of degree $k$ and $\phi$ is a linear combination of functions of shape $x^c$, $c\not \in \mathbb{N}$, $1 0$ being an explicitly given rational function in $k$.

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Paolo Minelli. 2021-10-08. On small fractional parts of perturbed polynomials. https://arxiv.org/abs/2110.04167

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