On a Theorem of Legendre on Diophantine Approximation

2024/07/15 by Jaroslav Hančl, Hančl, Jaroslav, Tho Phuoc Nguyen +1
Mathematics · Physics and Astronomy · #11A55 #11J82 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2407.11166

openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Legendre's theorem states that every irreducible fraction (p)/(q) which satisfies the inequality |α-(p)/(q) | < (1)/(2q²) is convergent to α. Later Barbolosi and Jager improved this theorem. In this paper we refine these results.

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