A century of metric Diophantine approximation and half a decade since Koukoulopoulos-Maynard
Number Theory
2025-05-15 v1
Abstract
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 breakthroughs in this area. We focus particularly on the direction of the Duffin-Schaeffer Conjecture which was spectacularly proven in 2020. We present some simplified key ideas of the proof that can also be applied in various other areas of number theory.
Keywords
Cite
@article{arxiv.2505.08901,
title = {A century of metric Diophantine approximation and half a decade since Koukoulopoulos-Maynard},
author = {Manuel Hauke},
journal= {arXiv preprint arXiv:2505.08901},
year = {2025}
}
Comments
25 pages; survey article to appear in Internationale Mathematische Nachrichten