Introduction to Algebraic Independence Theory

• Corporate Author: SpringerLink (Online service)
• Other Authors: Nesterenko, Yuri V. (Editor, http://id.loc.gov/vocabulary/relators/edt), Philippon, Patrice (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 1st ed. 2001.
• Series: Lecture Notes in Mathematics, 1752
• Subjects: Number theory.; Algebraic geometry.; Number Theory.; Algebraic Geometry.

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...

Table of Contents:

• ?(?, z) and Transcendence
• Mahler's conjecture and other transcendence Results
• Algebraic independence for values of Ramanujan Functions
• Some remarks on proofs of algebraic independence
• Elimination multihomogene
• Diophantine geometry
• Géométrie 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 II: Large Transcendence Degrees
• Some metric results in Transcendental Numbers Theory
• The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence.