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Transcendental numbers /

Bibliographic Details
Main Author: Murty, Maruti Ram
Other Authors: Rath, Purusottam
Format: Book
Language:English
Published: New York : Springer, [2014]
Subjects:
Transcendental numbers.
Table of Contents:
  • 1. Liouville's theorem
  • 2. Hermite's theorem
  • 3. Lindemann's theorem
  • 4. The Lindemann-Weierstrass theorem
  • 5. The maximum modulus principle and its applications
  • 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. 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 class group L-functions
  • 27. Transcendence of values of modular forms
  • 28. Periods, multiple zeta functions and [zeta](3).