Algebraic Independence is an expanded version of the notes of a course of lectures given by Professor Yuri V. Nesterenko at TIFR. It deals with several important results and methods in Transcendental Number Theory. The main results which are proved in detail are the classical result of Lindemann-Weierstrass, Siegel’s theory of E-functions and Shidlovskii’s theorem on the algebraic independence of the values of the E-functions, the Gelfond-Schneider Theorem using interpolation determinants and the famous result of the author in 1996 on the algebraic independence of the values of the Ramanujan functions. The book is self-contained and the proofs are clear and lucid. Brief history of the topics is also given.

Preface / Lindemann-Weierstrass Theorem / E-functions and Shidlovskii’s Theorem / Small Transcendence Degree (Exponential Function) / Small Transcendence Degree (Modular Functions) / Algebraic Fundamentals / Philippon’s Criterion of Algebraic Independence / Fields of Large Transcendence Degree / Multiplicity Estimates / Bibliography / Index.

Postgraduate Students and Researchers in Mathematics