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Introduction to algebraic independence theory /

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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 algebrai...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Nesterenko, I︠U︡riĭ Valentinovich, Philippon, Patrice, 1954-
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [2001]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1752.
Subjects:
Algebraic independence.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • PHI(tau, z) and Transcendence
  • Mahler's conjecture and other transcendence results
  • Algebraic independence for values of Ramanujan functions
  • Some remarks in proofs of algebraic independence
  • limination multihomogne
  • Diophantine geometry
  • Gomtrie diophantienne multiprojective
  • Criteria for algebraic independence
  • Upper bounds for (geometric) Hilbert functions
  • Multiplicity estimates for solutions of algebraic differential equations
  • Zero Estimates on Commutative Algebraic Groups
  • Measures of algebraic independence for Mahler functions
  • Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees
  • Algebraic Independence in Algebraic Groups. Part 2: Large Transcendence Degrees
  • Some metric results in Transcendental Numbers Theory
  • The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence.