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### S-integral points on hyperelliptic curves

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Gallegos-Ruiz, Homero R..
(2011)
*S-integral points on hyperelliptic curves.*
International Journal of Number Theory, Volume 7
(Number 3).
p. 803.
ISSN 1793-0421

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1142/S1793042111004435

## Abstract

Let C : Y(2) = a(n)X(n) + ... + a(0) be a hyperelliptic curve with the a(i) rational integers, n >= 5, and the polynomial on the right irreducible. Let J be its Jacobian. Let S be a finite set of rational primes. We give a completely explicit upper bound for the size of the S-integral points on the model C, provided we know at least one rational point on C and a Mordell-Weil basis for J(Q). We use a refinement of the Mordell-Weil sieve which, combined with the upper bound, is capable of determining all the S-integral points. The method is illustrated by determining the S-integral points on the genus 2 hyperelliptic model Y(2) - Y = X(5) - X for the set S of the first 22 primes.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Curves, Integrals, Hyperelliptic |

Journal or Publication Title: | International Journal of Number Theory |

Publisher: | World Scientific Publishing Co. Pte. Ltd. |

ISSN: | 1793-0421 |

Official Date: | 2011 |

Volume: | Volume 7 |

Number: | Number 3 |

Page Range: | p. 803 |

Identification Number: | 10.1142/S1793042111004435 |

Status: | Peer Reviewed |

Publication Status: | Published |

Funder: | Consejo Nacional de Ciencia y Tecnología (Mexico) [Mexican Council for Science and Technology] (CONACYT) |

Grant number: | 160194 (CONACYT) |

References: | [1] A. Baker, Bounds for the solutions of the hyperelliptic equation, Math. Proc. Cambridge |

URI: | http://wrap.warwick.ac.uk/id/eprint/41337 |

Data sourced from Thomson Reuters' Web of Knowledge

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