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Algebraic Independence
Author(s): Yu. V. Nesterenko

ISBN:    978-81-7319-984-4 
Publication Year:   Reprint 2011
Pages:   160
Binding:   Paper Back
Dimension:   160mm x 240mm
Weight:   300



About the book

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, Siegelís theory of E-functions and Shidlovskiiís 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.



Table of Contents

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




Audience

Postgraduate Students and Researchers in Mathematics


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