On a Theorem of Nathanson on Diophantine Approximation

Jaroslav Hančl; Tho Phuoc Nguyen

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arXiv · 2407.11525

On a Theorem of Nathanson on Diophantine Approximation

Jaroslav Hančl·Tho Phuoc Nguyen

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Abstract

In 1974, M. B. Nathanson proved that every irrational number $\alpha$ 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 $|\alpha-p/q|<1/(\sqrt{k^2+4}q^2)$. In this paper we refine this result.

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Jaroslav Hančl, Tho Phuoc Nguyen. 2024-07-16. On a Theorem of Nathanson on Diophantine Approximation. https://arxiv.org/abs/2407.11525

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