Institut de Mathématiques de Luminy, CNRS, 163 Avenue de Luminy, Case 907, 13288 Marseille Cédex 9, France ; Département de Mathématiques, Université d'Ottawa, 585 King Edward, Ottawa, Ontario, Canada K1N 6N5
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.