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On Baker's inequality for linear forms in logarithms

Published online by Cambridge University Press:  24 October 2008

Alfred J. van der Poorten
Alfred J. van der Poorten
Affiliation:
University of New South Wales
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Abstract

Let α1, …, αn an be non-zero algebraic numbers with degrees at most d and heights respectively Al, …, An (all Aj ≥ 4) and let b1, …, bn be rational integers with absolute values at most B (≥ 4). Denote by p a prime ideal of the field and suppose that p divides the rational prime p. Write

Then it is shown that

for some effectively computable constant C > 0 depending only on n, d and p. The argument suffices to prove similarly that in the complex case, if

for any fixed determination of the logarithms, then

for some effectively computable constant C′ > 0 depending only on n and d (and he determination of the logarithms).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 233 - 248
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

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