2025/02/02 by Shivani Goel, Rashi Lunia, Goel, Shivani +3
Mathematics · #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #math.NT
paper · pdf · doi:10.48550/arxiv.2502.00731
openalex publication_date 2025/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.