Manuel Hauke

activity

20232026

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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…