arXiv subjects

Tho Phuoc Nguyen

Publications and source records attributed to Tho Phuoc Nguyen.

2 recordsLinked to original sources

arXiv2024

On a Theorem of Nathanson on Diophantine Approximation

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 $|α-p/q|<1/(\sqrt{k^2+4}q^2)$. In this paper we refine this result.

math.NT↗

arXiv2024

On a Theorem of Legendre on Diophantine Approximation

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

math.NT↗