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arXiv · 2407.11166

On a Theorem of Legendre on Diophantine Approximation

Jaroslav Hančl·Tho Phuoc Nguyen
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Abstract

Legendre's theorem states that every irreducible fraction $\frac{p}{q}$ which satisfies the inequality $\left |\alpha-\frac{p}{q} \right | < \frac{1}{2q^2}$ is convergent to $\alpha$. Later Barbolosi and Jager improved this theorem. In this paper we refine these results.

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Jaroslav Hančl, Tho Phuoc Nguyen. 2024-07-15. On a Theorem of Legendre on Diophantine Approximation. https://arxiv.org/abs/2407.11166

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