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An effective lower bound on the “Diophantine approximation” of algebraic functions by rational functions

Published online by Cambridge University Press:  26 February 2010

Charles F. Osgood
Charles F. Osgood
Affiliation:
Mathematics Research Center, Naval Research Laboratory, Washington, D.C., 20375.
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Extract

The idea of obtaining bounds on the order of approximation of algebraic functions by rational functions apparently goes back to Maillet [8]. It is very easy, using an argument analogous to that used by Liouville for algebraic numbers, to see that if w(z) is any algebraic function of degree n ≥ 2 over Q[z] then for all pairs of polynomials r(z) and s(z) with s(z) ≢ 0 we have

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Type
Research Article
Information
Mathematika , Volume 20 , Issue 1 , June 1973, pp. 4 - 15
Copyright
Copyright © University College London 1973

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References

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