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Published online by Cambridge University Press: 09 April 2009
Let …, αn, (n ≧ 2) be (fixed) multiplicatively independent non zero algebraic numbers and set M(H) = min |β1log α1+…+βn log αn| the minimum taken over all algebraic numbers bgr;1,…βn not all equal to zero, of degrees not exceeding a fixed natural number d0, and heights not exceeding an arbitrary natural number H. Then an important result [1] of Baker states that 
for every fixed ε > 0 and an explicit constant 
. It may be remarked that Baker deduces his general result from the special case where βn is fixed to be —1. The following straight forward generalization might be of some interest since it shows that the exponent n+1+ε need not be the best, and that the best exponent obtainable by his method has some chance of being 1 + ε (see the corollary to the Theorem).
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