On a Theorem of Nathanson on Diophantine Approximation

2024/07/16 by Jaroslav Hančl, Hančl, Jaroslav, Tho Phuoc Nguyen +1 · 1 citation
Mathematics · #11A55 #11J82 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2407.11525

openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1974, M. B. Nathanson proved that every irrational number α represented by a simple continued fraction with infinitely many elements greater than or equal to k is approximable by an infinite number of rational numbers p/q satisfying |α-p/q|<1/(√(k²+4)q²). In this paper we refine this result.

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