Sums of nearest integer continued fractions with bounded digits: $\textrm{NICF}_5 + \textrm{NICF}_5 = {\mathbb R}$
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917961430728704 |
|---|---|
| author | Bosma, Wieb Brouwers, Alex |
| author_facet | Bosma, Wieb Brouwers, Alex |
| contents | Adapting Cantor set methods that were used by Hall and Hlawka for regular continued fractions, we prove that every real number can be obtained as the sum of two real numbers for which the partial fractions in their nearest integer continued fraction expansion do not exceed 5 (with the zeroth partial fraction as the only possible exception). Furthermore, we prove that it is not possible to replace 5 by 4 in this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sums of nearest integer continued fractions with bounded digits: $\textrm{NICF}_5 + \textrm{NICF}_5 = {\mathbb R}$ Bosma, Wieb Brouwers, Alex Number Theory 11A55 Adapting Cantor set methods that were used by Hall and Hlawka for regular continued fractions, we prove that every real number can be obtained as the sum of two real numbers for which the partial fractions in their nearest integer continued fraction expansion do not exceed 5 (with the zeroth partial fraction as the only possible exception). Furthermore, we prove that it is not possible to replace 5 by 4 in this result. |
| title | Sums of nearest integer continued fractions with bounded digits: $\textrm{NICF}_5 + \textrm{NICF}_5 = {\mathbb R}$ |
| topic | Number Theory 11A55 |
| url | https://arxiv.org/abs/2503.15097 |