Abstract
In this paper, we obtain an explicit form of the currently best known inequality for linear forms in the logarithms of algebraic numbers. The results complete our previous investigations (Bull. Austral. Math. Soc. 15 (1976), 33–57) which were conditional on a certain independence condition on the algebraic numbers. The extra work needed to obtain unconditional results centres on the properties of multiplicative relations in number fields. In particular, we show that a set of multiplicatively dependent algebraic numbers always satisfies a relation with relatively small exponents.
| Original language | English |
|---|---|
| Pages (from-to) | 83-98 |
| Number of pages | 16 |
| Journal | Bulletin of the Australian Mathematical Society |
| Volume | 16 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1977 |
| Externally published | Yes |
Bibliographical note
Corrigendum and addendum 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
van der Poorten, A. J., & Loxton, J. H. (1977). Multiplicative relations in number fields. Bulletin of the Australian Mathematical Society, 16(1), 83-98. https://doi.org/10.1017/S0004972700023042