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Transcendental numbers / M. Ram Murty, Purusottam Rath.

By: Murty, Maruti Ram.
Contributor(s): Rath, Purusottam.
Material type: TextTextPublisher: New York : Springer, [2014]Copyright date: ©2014Description: xiv, 217 pages ; E 51.99 24 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781493908318 (alk. paper); 1493908316 (alk. paper).Subject(s): Transcendental numbers | Transcendental numbers
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).
Abstract: 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.-- Source other than Library of Congress.
List(s) this item appears in: 2015-03-24
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		512.73 MUR (Browse shelf) Checked out 17/06/2024 9499
Total holds: 0

Includes bibliographical references (pages 205-213) and index.

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).

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.-- Source other than Library of Congress.