Approximations diophantiennes et nombres transcendants : colloque de Luminy, (13-19 juin) 1982 : (comptes-rendus du Colloque "Problèmes diophantiens")

This volume contains proceedings of the 1982 Conference on Diophantine Approximations held in Luminy, France, as well as survey articles on related topics. Considerable progress in this field has been made recently by the introduction of methods from algebraic geometry and from the theory of differential equations. The application of these methods to problems of linear or algebraic independence and to irrationality measures forms the central theme of this book. Recent advances and open problems are included. This volume will be of interest to professional and graduate level number theory specialists. TABLE DES MATIERES Préface vii ENDOMORPHISMES DE GROUPES ALGEBRIQUES; APPLICATIONS ARITHMÉTIQUES D. Bertrand 1 IRRATIONALITY OF 7T2, PERIODS OF AN ELLIPTIC CURVE AND r (5) F. Beukers 47 ZERO ESTIMATES FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS W.D. Brownawell 67 SUR DES ESTIMATIONS PRECISES PAR RAPPORT A LA HAUTEUR DE CERTAINES FORMES LINEAIRES A.I. Galockin 95 FONCTIONS ENTIÈRES ARITHMETIQUES F. Gramain et M. Mignotte 99 THÉORIE DE KUMMER SUR UNE EXTENSION D'UNE COURBE ELLIPTIQUE PAR