On a Theorem of Legendre on Diophantine Approximation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909256830156800 |
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| author | Hančl, Jaroslav Nguyen, Tho Phuoc |
| author_facet | Hančl, Jaroslav Nguyen, Tho Phuoc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Theorem of Legendre on Diophantine Approximation Hančl, Jaroslav Nguyen, Tho Phuoc Number Theory 11J82, 11A55 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. |
| title | On a Theorem of Legendre on Diophantine Approximation |
| topic | Number Theory 11J82, 11A55 |
| url | https://arxiv.org/abs/2407.11166 |