Diophantine approximation and the subspace theorem
Abstract
Diophantine approximation explores how well irrational numbers can be approximated by rationals, with foundational results by Dirichlet, Hurwitz, and Liouville culminating in Roth's theorem. Schmidt's subspace theorem extends Roth's results to higher dimensions, with profound implications to Diophantine equations and transcendence theory. This article provides a self-contained and accessible exposition of Roth's theorem and Schlickewei's refinement of the subspace theorem, with an emphasis on proofs. The arguments presented are classical and approachable for readers with a background in algebraic number theory, serving as a streamlined, yet condensed reference for these fundamental results.
Cite
@article{arxiv.2502.00731,
title = {Diophantine approximation and the subspace theorem},
author = {Shivani Goel and Rashi Lunia and Anwesh Ray},
journal= {arXiv preprint arXiv:2502.00731},
year = {2025}
}
Comments
Version 1: 49 pages. This article originated from material presented at the workshop "The Subspace Theorem and Its Applications", held at the Chennai Mathematical Institute from December 16 to 28, 2024, where the third author was a speaker