Simultaneous approximation of numbers connected with the exponential function
- 1 June 1978
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 25 (4) , 466-478
- https://doi.org/10.1017/s1446788700021443
Abstract
We give several results concerning the simultaneous approximation of certain complex numbers. For instance, we give lower bounds for |a–ξo|+ |ea– ξ1|, whereais 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.Keywords
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