Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T21:11:10.636Z Has data issue: false hasContentIssue false

Linear forms in the logarithms of algebraic numbers (II)

Published online by Cambridge University Press:  26 February 2010

A. Baker
Affiliation:
Trinity College, Cambridge.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)