Number Theory IV: Transcendental Numbers

A.N. Parshin, I.R. Shafarevich, N. Koblitz, N.I. Fel’dman, Yu.V. Nesterenko3540614672, 9783540614678

This book is a survey of the most important directions of research in transcendental number theory – the theory of irrationality, transcendence, and algebraic independence of various numbers. There is a special emphasis on the transcendence properties of the values of special functions. The book contains few complete proofs, but rather gives conceptual discussions of the central ideas behind the proofs. For a reader who has no specific background in transcendental number theory the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.