Chapter 4: Transcendence and algebraic independence of the values of Ε-functions which are connected by algebraic equations over the field of rational functions

Kapitel in diesem Buch

1. Frontmatter I
2. Foreword V
3. Preface to the English edition IX
4. Preface XI
5. Notation XVIII
6. Introduction 1
7. Chapter 1: Approximation of real and algebraic numbers 11
8. Chapter 2: Arithmetic properties of the values of the exponential function at algebraic points 41
9. Chapter 3: Transcendence and algebraic independence of the values of Ε-functions which are not connected by algebraic equations over the field of rational functions 79
10. Chapter 4: Transcendence and algebraic independence of the values of Ε-functions which are connected by algebraic equations over the field of rational functions 128
11. Chapter 5: Transcendence and algebraic independence of the values of Ε-functions which satisfy first order linear differential equations 179
12. Chapter 6: Algebraic independence of the values of E-functions which satisfy second order linear differential equations 207
13. Chapter 7: Solutions of certain linear differential equations of arbitrary order 232
14. Chapter 8: Arithmetic methods applied to solutions of linear differential equations of arbitrary order 249
15. Chapter 9: Siegel's Theorem 271
16. Chapter 10: Solutions of linear differential equations of prime order p 307
17. Chapter 11: The algebraic independence measure of values of IE-functions 349
18. Chapter 12: The algebraic independence measure of values of KE-functions 378
19. Chapter 13: Effective bounds for measures 405
20. Concluding remarks 436
21. Supplementary remarks on recent work for the English edition 444
22. Bibliography 452
23. Backmatter 467