On continued fraction expansions of quadratic irrationals in positive characteristic
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866908617465135104 |
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| author | Paulin, Frédéric Shapira, Uri |
| author_facet | Paulin, Frédéric Shapira, Uri |
| contents | Let $P$ be a prime polynomial in the variable $Y$ over a finite field and let $f$ be a quadratic irrational in the field of formal Laurant series in the variable $Y^{-1}$. We study the asymptotic properties of the degrees of the coefficients of the continued fraction expansion of quadratic irrationals such as $P^nf$ and prove results that are in sharp contrast to the analogue situation in zero characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_10184 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On continued fraction expansions of quadratic irrationals in positive characteristic Paulin, Frédéric Shapira, Uri Dynamical Systems Number Theory Let $P$ be a prime polynomial in the variable $Y$ over a finite field and let $f$ be a quadratic irrational in the field of formal Laurant series in the variable $Y^{-1}$. We study the asymptotic properties of the degrees of the coefficients of the continued fraction expansion of quadratic irrationals such as $P^nf$ and prove results that are in sharp contrast to the analogue situation in zero characteristic. |
| title | On continued fraction expansions of quadratic irrationals in positive characteristic |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/1801.10184 |