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  • Book
  • © 2001

Introduction to Algebraic Independence Theory

  • The first didactically-conceived presentation of the recent development in transcendence theory

  • Includes supplementary material: sn.pub/extras

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

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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.

Keywords

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

Editors and Affiliations

  • Faculty of Mechanics and Mathematics, Moscow University, Moscow, Russia

    Yuri V. Nesterenko

  • Institut de Mathématiques de Jussieu, UMR 7586 du CNRS, Paris Cedex 05, France

    Patrice Philippon

Bibliographic Information

  • Book Title: Introduction to Algebraic Independence Theory

  • Editors: Yuri V. Nesterenko, Patrice Philippon

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b76882

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Softcover ISBN: 978-3-540-41496-4Published: 18 January 2001

  • eBook ISBN: 978-3-540-44550-0Published: 01 July 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 260

  • Topics: Number Theory, Algebraic Geometry

Buying options

eBook USD 44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions