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Multiplicative relations in number fields

Published online by Cambridge University Press:  17 April 2009

A.J. van der Poorten  and
J.H. Loxton
A.J. van der Poorten
Affiliation:
School' of Mathematics, University of New South Wales, Kensington, New South Wales.
J.H. Loxton
Affiliation:
School' of Mathematics, University of New South Wales, Kensington, New South Wales.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 1 , February 1977 , pp. 83 - 98
Copyright
Copyright © Australian Mathematical Society 1977

References

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