Criteria of algebraic independence with multiplicities and interpolation determinants
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- by Michel Laurent and Damien Roy PDF
- Trans. Amer. Math. Soc. 351 (1999), 1845-1870 Request permission
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.References
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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
- MR Author ID: 265895
- Email: droy@mathstat.uottawa.ca
- Received by editor(s): March 12, 1997
- Published electronically: January 19, 1999
- Additional Notes: Second author partially supported by NSERC and CICMA
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 1845-1870
- MSC (1991): Primary 11J85; Secondary 11J04
- DOI: https://doi.org/10.1090/S0002-9947-99-02216-3
- MathSciNet review: 1475689