Contributions

  • F. Amoroso (Contributor) - Contributor
  • D. Bertrand (Contributor) - Contributor
  • W.D. Brownawell (Contributor) - Contributor
  • G. Diaz (Contributor) - Contributor
  • M. Laurent (Contributor) - Contributor
and 8 more
  • Yu.V. Nesterenko (Contributor) - Contributor
  • K. Nishioka (Contributor) - Contributor
  • P. Philippon (Contributor) - Contributor
  • G. Remond (Contributor) - Contributor
  • D. Roy (Contributor) - Contributor
  • M. Waldschmidt (Contributor) - Contributor
  • Yuri V. Nesterenko (Editor) - Contributor
  • Patrice Philippon (Editor) - Contributor

Publication

2001-02-23 - Springer

Language

English

Word Count

64,000 words, Guess

Page Count

256 pages

Physical Format

Paperback

Identifiers

and 2 more
  • Library of Congress Control Number00054757
  • Goodreads4291849

Classifications

  • LCCQA3 .L28 no. 1752

Description

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.

First Sentence

The first two sections of this Chapter are devoted to the differential properties of modular forms on which Nesterenko's theorem on the values of Eisenstein series (see Chapter 3, Theorem 1.1 and [Nes9]) is based.

Subjects

Topics

Other Editions

  • Introduction to Algebraic Independence Theory (Lecture Notes in Mathematics)PaperbackSpringer2001-02-23

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