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Linear forms in the logarithms of algebraic numbers (II)

Published online by Cambridge University Press:  26 February 2010

A. Baker
Affiliation:
Trinity College, Cambridge.
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Extract

It was proved in a recent paper† that if au α1, …, αn denote non-zero algebraic numbers and if‡ logαn, …, log αn and and 2πi are linearly independent over the rationals then log α1, …, log αn are linearly independent over the field of all algebraic numbers. Further it was shown that if α1 …, αn are positive real algebraic numbers other than 1 and if β1, …, βn denote real algebraic numbers with 1, β1 …, βn linearly independent over the rationals then is transcendental.

Type
Research Article
Copyright
Copyright © University College London 1967

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