### Abstract

For certain number theoretical applications, it is useful to actually compute the effectively computable constant which appears in Baker's inequality for linear forms in logarithms. In this note, we carry out such a detailed computation, obtaining bounds which are the best known and, in some respects, the best possible. We show inter alia that if the algebraic numbers α_{1}, …, α_{n} all lie in an algebraic number field of degree D and satisfy a certain independence condition, then for some n_{0}(D) which is explicitly computed, the inequalities (in the standard notation) [formula omitted] have no solution in rational integers b_{1}, …, b_{n} (b_{n} ≠ 0) of absolute value at most B, whenever n ≥ n_{0}(D). The very favourable dependence on n is particularly useful.

Original language | English |
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Pages (from-to) | 33-57 |

Number of pages | 25 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 15 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1976 |

Externally published | Yes |

### Bibliographical note

Corrigenda and addenda can be found in Bulletin of the Australian Mathematical Society, 17(1), pp. 151-155, 1977.https://doi.org/10.1017/S0004972700025600

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## Cite this

*Bulletin of the Australian Mathematical Society*,

*15*(1), 33-57. https://doi.org/10.1017/S0004972700036741