Manuel Hauke

activity

20242026

collaborators

7 papers

math.NT2026

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.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 $I^\pm$ and monotonically decreasing $I ¨ $ a Khintchine-type statement on the set of the inhomogeneous rea…

math.NT2025

Twisted approximation with restricted denominators

Manuel Hauke, Felipe A. RamÃrez

Given an increasing integer sequence $(a_{n})$ , a real number $I^\pm$ , and a sequence $I ¨ (n)$ , we study the set $W$ of real numbers $I^^{3}$ for which $a_{n} I^\pm - I^^{3}$ is a distance less than $Ï…

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…