Manuel Hauke

activity

20232026

collaborators

8 papers

math.NT2026

Circle coverings driven by arithmetic sequences: a percolation approach to Diophantine approximation and fractal intersections

Manuel Hauke, Andrei Shubin, Eduard Stefanescu +1

We study problems on covering $[0, 1)$ by shrinking intervals centered at the points ${q_{n} x}$ , where $(q_{n})_{n \in N}$ is a given real-valued sequence and $x \in [0, 1)$ i…

math.NT2026

The Prime times of twisted Diophantine approximation

Manuel Hauke

The seminal work of Kurzweil (1955) provides for any fixed badly approximable $α$ and monotonically decreasing $ψ$ a Khintchine-type statement on the set of the inhomogeneous real…

math.NT2025

Twisted approximation with restricted denominators

Manuel Hauke, Felipe A. Ramírez

Given an increasing integer sequence $(a_{n})$ , a real number $α$ , and a sequence $ψ (n)$ , we study the set $W$ of real numbers $γ$ for which $a_{n} α - γ$ is a distance less than $ψ (n)$ …

math.NT2025

A century of metric Diophantine approximation and half a decade since Koukoulopoulos-Maynard

Manuel Hauke

In this note, we review the history of Khintchine's Theorem which is the foundation of metric Diophantine approximation, and discuss several generalizations and recent breakthrough…

math.NT2025

General Duffin--Schaeffer-type counterexamples in diophantine approximation

Sam Chow, Manuel Hauke, Andrew Pollington +1

Duffin and Schaeffer provided a famous counterexample to show that Khintchine's theorem fails without monotonicity assumption. Given any monotonically decreasing approximation func…

math.NT2024

Borel-Cantelli, zero-one laws and inhomogeneous Duffin-Schaeffer

Victor Beresnevich, Manuel Hauke, Sanju Velani

The most versatile version of the classical divergence Borel-Cantelli lemma shows that for any divergent sequence of events $E_{n}$ in a probability space satisfying a quasi-independ…

math.NT2024

Proving the Duffin-Schaeffer conjecture without GCD graphs

Manuel Hauke, Santiago Vazquez Saez, Aled Walker

We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthroug…

math.NT2023

Rational approximation with chosen numerators

Emmanuel Kowalski

We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We then present a simple…