Introduction to Algebraic Independence Theory

  • Yuri V. Nesterenko
  • Patrice Philippon

Part of the Lecture Notes in Mathematics book series (LNM, volume 1752)

About this book

Introduction

In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.

Keywords

Algebraic independence Dimension algebra algebraic geometry algebraic group commutative algebra elimination modular form modular forms multiplicity estimates transcendence

Editors and affiliations

  • Yuri V. Nesterenko
    • 1
  • Patrice Philippon
    • 2
  1. 1.Faculty of Mechanics and MathematicsMoscow UniversityMoscowRussia
  2. 2.Institut de Mathématiques de JussieuUMR 7586 du CNRSParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/b76882
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-41496-4
  • Online ISBN 978-3-540-44550-0
  • Series Print ISSN 0075-8434
  • About this book