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Simultaneous diophantine approximations and Hermite's method

Published online by Cambridge University Press:  17 April 2009

Alain Durand
Alain Durand
Affiliation:
UER des Sciences de Limoges, Départment de Mathématiques, 123 rue Albert Thomas, 87100 Limoges, France.
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In this paper we generalize a result of Mahler on rational approximations of the exponential function at rational points by proving the following theorem: let n ε N* and αl, …, αn be distinct non-zero rational numbers; there exists a constant c = c(n, αl, …, αn) ≥ 0 such that

for every non-zero integer point (qo, ql, …, qn)and q = max {|ql|, … |qn|, 3}.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 3 , June 1980 , pp. 463 - 470
Copyright
Copyright © Australian Mathematical Society 1980

References

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