© 2001

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


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.


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

  • Book Title Introduction to Algebraic Independence Theory
  • Editors Yuri V. Nesterenko
    Patrice Philippon
  • Series Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-41496-4
  • eBook ISBN 978-3-540-44550-0
  • Series ISSN 0075-8434
  • Edition Number 1
  • Number of Pages XVI, 260
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Algebraic Geometry
  • Buy this book on publisher's site
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