Simultaneous Approximation of Logarithms of Algebraic Numbers

Recently, close connections have been established between simultaneous diophantine approximation and algebraic independence. A survey of this topic is given by M. Laurent in these proceedings [7]. These connections are one of the main motivations to investigate systematically the question of algebraic approximation to transcendental numbers. In view of the applications to algebraic independence, a special attention is paid to the dependence on the degree. To each qualitative transcendence result telling: one at least of the numbers θ1, . . . , θm is transcendental one can associate a quantitative refinement, which is a lower bound for