Book in preparation:

Diophantine Approximation on

Linear Algebraic Groups

(Transcendence Properties of the Exponential Function
in Several Variables)  

Table of Contents
 

1. Introduction and Historical Survey

 

Part I. Linear Independence of Logarithms of Algebraic Numbers
2. Transcendence Proofs in One Variable
3. Heights of Algebraic Numbers
4. The Criterion of Schneider-Lang

 

Part II. Linear Independence of Logarithms and Measures

5. Zero Estimate, by Damien ROY
6. Linear Independence of Logarithms of Algebraic Numbers
7. A First Measure of Linear Independence
 

III. Multiplicities in Higher Dimension


8. Multiplicity Estimates, by Damien ROY
9. Interpolation Determinants with One Derivative
10. On Baker's Method
 

Part IV. The Linear Subgroup Theorem


11. Points Whose Coordinates are Logarithms of Algebraic Numbers
12. Lower Bounds for the Rank of Matrices
 

Part V. Simultaneous Approximation of Values of the

Exponential Function in Several Variables

13. A Quantitative Version of the Linear Subgroup Theorem
14. Applications to Diophantine Approximation
15. Algebraic Independence
 

References


Michel Waldschmidt
URL : http://www.math.jussieu.fr/~miw/articles/DALAG.html
e-mail : miw@math.jussieu.fr
Last update : April 14, 1999