### Abstract

We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion. In the quartic and sextic cases we observe explicitly that the parameters appearing in the continued fraction expansion yield integer sequences defined by bilinear relations instancing sequences of Somos type.

Original language | English |
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Title of host publication | Dynamics & stochastics |

Subtitle of host publication | festschrift in Honour of M.S. Keane |

Editors | Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy |

Place of Publication | Beachwood, Ohio |

Publisher | Institute of Mathematical Statistics |

Pages | 212-224 |

Number of pages | 13 |

ISBN (Print) | 0940600641 |

DOIs | |

Publication status | Published - 2006 |

Event | Workshop on Dynamical systems, Probability theory, and Statistical Mehanics - Eindhoven, Netherlands Duration: 3 Jan 2005 → 7 Jan 2005 |

### Publication series

Name | Lecture notes-monograph series |
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Publisher | Institute of Mathematical Statistics |

Volume | 48 |

### Workshop

Workshop | Workshop on Dynamical systems, Probability theory, and Statistical Mehanics |
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City | Eindhoven, Netherlands |

Period | 3/01/05 → 7/01/05 |

### Keywords

- continued fraction expansion
- function field of characteristic zero
- hyperelliptic curve
- Somos sequence

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## Cite this

van der Poorten, A. J. (2006). Hyperelliptic curves, continued fractions, and Somos sequences. In D. Denteneer, F. den Hollander, & E. Verbitskiy (Eds.),

*Dynamics & stochastics: festschrift in Honour of M.S. Keane*(pp. 212-224). (Lecture notes-monograph series; Vol. 48). Beachwood, Ohio: Institute of Mathematical Statistics. https://doi.org/10.1214/074921706000000239