Paolo Minelli

collaborators

3 papers

math.NT2021

On small fractional parts of perturbed polynomials

Paolo Minelli

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 Madrit…

math.NT2021

On small fractional parts of polynomial-like functions

Paolo Minelli

In a recent paper, Madritsch and Tichy established Diophantine inequalities for the fractional parts of polynomial-like functions. In particular, for $f (x) = x^{k} + x^{c}$ where $k$ is a…

math.NT2019

On the number of gaps of sequences with Poissonian Pair Correlations

Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti +1

A sequence $(x_{n})$ on the torus is said to have Poissonian pair correlations if $# {1 \leq i \neq = j \leq N : ∣ x_{i} - x_{j} ∣ \leq s / N} = 2 s N (1 + o (1))$ for all reals $s > 0$ , as $N \to \infty$ . It…