Multiplicative relations in number fields

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

doi:10.1017/S0004972700023042

Multiplicative relations in number fields

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

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

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	https://doi.org/10.1017/S0004972700023042
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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10.1017/S0004972700023042

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