Transcendental Numbers
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book fo...
| Κύριοι συγγραφείς: | , |
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| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
New York, NY :
Springer New York : Imprint: Springer,
2014.
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| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 1. Liouville’s theorem
- 2. Hermite’s Theorem
- 3. Lindemann’s theorem
- 4. The Lindemann-Weierstrass theorem
- 5. The maximum modulus principle
- 6. Siegel’s lemma
- 7. The six exponentials theorem
- 8. Estimates for derivatives
- 9. The Schneider-Lang theorem
- 10. Elliptic functions
- 11. Transcendental values of elliptic functions
- 12. Periods and quasiperiods
- 13. Transcendental values of some elliptic integrals
- 14. The modular invariant
- 15. Transcendental values of the j-function
- 16. More elliptic integrals
- 17. Transcendental values of Eisenstein series
- 18. Elliptic integrals and hypergeometric series
- 19. Baker’s theorem
- 20. Some applications of Baker’s theorem
- 21. Schanuel’s conjecture
- 22. Transcendental values of some Dirichlet series
- 23. Proof of the Baker-Birch-Wirsing theorem
- 24. Transcendence of some infinite series
- 25. Linear independence of values of Dirichlet L-functions
- 26. Transcendence of values of modular forms
- 27. Transcendence of values of class group L-functions
- 28. Periods, multiple zeta functions and (3). .
