Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function esubz. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions with a discussion of Lehmer's problem, several proofs of Bak...