## Title data

Bugeaud, Yann ; Mignotte, Maurice ; Siksek, Samir ; Stoll, Michael ; Tengely, Szabolcs:

**Integral points on hyperelliptic curves.**

*In:* Algebra & Number Theory.
Vol. 2
(2008)
Issue 8
.
- pp. 859-885.

ISSN 1937-0652

DOI: https://doi.org/10.2140/ant.2008.2.859

## Abstract in another language

Let C: Y2=a_n X^n+...+a_0 be a hyperelliptic curve with the a_i rational integers, n≥5, and the polynomial on the right-hand side irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the 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 also explain a powerful refinement of the Mordell-Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on the genus 2 hyperelliptic models Y^2-Y=X^5-X and binom(Y,2)=binom(X,5).

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | curve; integral point; Jacobian; height; Mordell-Weil group; Baker’s bound; Mordell-Weil sieve |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 26 Jan 2015 09:41 |

Last Modified: | 26 Jan 2015 09:41 |

URI: | https://eref.uni-bayreuth.de/id/eprint/5998 |