Introduction to Algebraic Independence Theory

Θ(τ, z ) and Transcendence....Pages 1-11
Mahler’s conjecture and other transcendence Results....Pages 13-26
Algebraic independence for values of Ramanujan Functions....Pages 27-46
Some remarks on proofs of algebraic independence....Pages 47-51
Elimination multihomogene....Pages 53-81
Diophantine geometry....Pages 83-94
Géométrie diophantienne multiprojective....Pages 95-131
Criteria for algebraic independence....Pages 133-141
Upper bounds for (geometric) Hilbert functions....Pages 143-148
Multiplicity estimates for solutions of algebraic differential equations....Pages 149-165
Zero Estimates on Commutative Algebraic Groups....Pages 167-185
Measures of algebraic independence for Mahler functions....Pages 187-197
Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees....Pages 199-211
Algebraic Independence in Algebraic Groups. Part II: Large Transcendence Degrees....Pages 213-225
Some metric results in Transcendental Numbers Theory....Pages 227-237
The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence....Pages 239-248