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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Effective irrationality measures for certain algebraic numbers


Author: David Easton
Journal: Math. Comp. 46 (1986), 613-622
MSC: Primary 11J68; Secondary 11J82
MathSciNet review: 829632
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Abstract: A result of Chudnovsky concerning rational approximation to certain algebraic numbers is reworked to provide a quantitative result in which all constants are explicitly given. More particularly, Padé approximants to the function $ {(1 - x)^{1/3}}$ are employed to show, for certain integers a and b, that

$\displaystyle \left\vert {{{(a/b)}^{1/3}} - p/q} \right\vert > c{q^{ - \kappa }}\quad {\text{when}}\,q > 0.$

Here, c and k are given as functions of a and b only.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0829632-4
PII: S 0025-5718(1986)0829632-4
Article copyright: © Copyright 1986 American Mathematical Society