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Simultaneous approximation of numbers connected with the exponential function

Published online by Cambridge University Press:  09 April 2009

Michel Waldschmidt
Michel Waldschmidt
Affiliation:
Université P. et M. Curie(Paris VI) Mathématiques, T45-46 4 Place Jussieu 75230 Paris Cedex 05, France
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Abstract

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We give several results concerning the simultaneous approximation of certain complex numbers. For instance, we give lower bounds for |a–ξo |+ | ea – ξ1 |, where a is any non-zero complex number, and ξ are two algebraic numbers. We also improve the estimate of the so-called Franklin Schneider theorem concerning | b – ξ | + | a – ξ | + | ab – ξ. We deduce these results from an estimate for linear forms in logarithms.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 4 , June 1978 , pp. 466 - 478
Copyright
Copyright © Australian Mathematical Society 1978

References

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