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Transcendental numbers M. Ram Murty, Purusottam Rath.

By: Contributor(s): Material type: TextTextPublication details: New York: Springer, 2014.Description: xiv, 217 pages ; 24 cmISBN:
  • 9781493908318 (alk. paper)
  • 1493908316 (alk. paper)
Subject(s): DDC classification:
  • 23 510 M96T
LOC classification:
  • QA247.5 .M87 2014
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.--
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Item type Current library Collection Call number Status Notes Date due Barcode
Books Books Central Library, IISER Bhopal Reference Section Reference 510 M96T (Browse shelf(Opens below)) Not For Loan Book recommended by Dr J. P. Saha 11432

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.--

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