The first and second moment for the length of the period of the continued fraction expansion for $\sqrt{d}$
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916336536387584 |
|---|---|
| author | Battistoni, Francesco Grenié, Loïc Molteni, Giuseppe |
| author_facet | Battistoni, Francesco Grenié, Loïc Molteni, Giuseppe |
| contents | Let $d$ be any positive and non square integer. We prove an upper bound for the first two moments of the length $T(d)$ of the period of the continued fraction expansion for $\sqrt{d}$. This allows to improve the existing results for the large deviations of $T(d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13118 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The first and second moment for the length of the period of the continued fraction expansion for $\sqrt{d}$ Battistoni, Francesco Grenié, Loïc Molteni, Giuseppe Number Theory 11A55, 11R11, 11Y65 Let $d$ be any positive and non square integer. We prove an upper bound for the first two moments of the length $T(d)$ of the period of the continued fraction expansion for $\sqrt{d}$. This allows to improve the existing results for the large deviations of $T(d)$. |
| title | The first and second moment for the length of the period of the continued fraction expansion for $\sqrt{d}$ |
| topic | Number Theory 11A55, 11R11, 11Y65 |
| url | https://arxiv.org/abs/2401.13118 |