Title | **All solutions to Thomas’ family of Thue equations over imaginary quadratic number fields** |

Author(s) | Clemens Heuberger |

Type | Article in Journal |

Abstract | We completely solve the family of relative Thue equations x^3 − ( t − 1 ) x^2 y − ( t + 2 ) x y^2 − y^3 = μ , where the parameter t , the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. This is achieved using the hypergeometric method for | t | ≥ 53 and Baker’s method combined with a computer search using continued fractions for the remaining values of t . |

Keywords | Relative Thue equation, Parametrized Thue equation, Hypergeometric method, Baker’s method reference |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717106000344 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 41 |

Number | 9 |

Pages | 980 - 998 |

Year | 2006 |

Edition | 0 |

Translation |
No |

Refereed |
No |