Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11J68, 11J82

Retrieve articles in all journals with MSC: 11J68, 11J82

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society