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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Criteria of algebraic independence with
multiplicities and interpolation determinants


Authors: Michel Laurent and Damien Roy
Journal: Trans. Amer. Math. Soc. 351 (1999), 1845-1870
MSC (1991): Primary 11J85; Secondary 11J04
Published electronically: January 19, 1999
MathSciNet review: 1475689
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Abstract | References | Similar Articles | Additional Information

Abstract: We generalize Gel'fond's criterion of algebraic independence by taking into account the values of the derivatives of the polynomials, and show how the new criterion applies to proving results of algebraic independence using interpolation determinants. We also establish a new result of approximation of a transcendental number by algebraic numbers of bounded degree and size. It contains an earlier result of E. Wirsing and also a result announced by A. Durand.


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Additional Information

Michel Laurent
Affiliation: Institut de Mathématiques de Luminy, CNRS, 163 Avenue de Luminy, Case 907, 13288 Marseille Cédex 9, France
Email: laurent@iml.univ-mrs.fr

Damien Roy
Affiliation: Département de Mathématiques, Université d’Ottawa, 585 King Edward, Ottawa, Ontario, Canada K1N 6N5
Email: droy@mathstat.uottawa.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02216-3
PII: S 0002-9947(99)02216-3
Received by editor(s): March 12, 1997
Published electronically: January 19, 1999
Additional Notes: Second author partially supported by NSERC and CICMA
Article copyright: © Copyright 1999 American Mathematical Society