Transcendental Numbers

2014
ISBN: 978-1-4939-0831-8
Verlag: Springer

Buch, Englisch, 217 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 3577 g

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 focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.

Zielgruppe

Graduate

Autoren/Hrsg.

Rath, Purusottam

Murty, M. Ram

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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).

Über Autor(innen)

M. Ram Murty is a professor of mathematics at Queen's University. Purusottam Rath is a professor of mathematics at the Chennai Mathematical Institute.