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

2025/05/13 by Hauke, Manuel · 1 citation
#11J83 11K60 11J04 11A05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.08901

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.

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