Multiplicative relations in number fields

A. J. van der Poorten, J. H. Loxton

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


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 languageEnglish
Pages (from-to)83-98
Number of pages16
JournalBulletin of the Australian Mathematical Society
Issue number1
Publication statusPublished - 1977
Externally publishedYes

Bibliographical note

Corrigendum and addendum can be found in Bulletin of the Australian Mathematical Society, 17(1), pp. 151-155, 1977.

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