- Provides a clear and accessible introduction to theorems relating to transcendental numbers
- Aimed at upper undergraduate and graduate students, as well as researchers seeking to familiarize themselves with the subject
- Touches on the Schneider-Lang theorem, elliptic curve theory, Baker's theorem, and their applications
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- About this Textbook
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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.
- About the authors
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M. Ram Murty is a professor of mathematics at Queen's University. Purusottam Rath is a professor of mathematics at the Chennai Mathematical Institute.
- Reviews
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From the book reviews:
“Transcendental Number Theory … though terse, has not had a significant competitor for nearly four decades, but the present volume by Murty (Queen’s Univ., Canada) and Rath (Chennai Mathematical Institute, India) surpasses it in certain ways. … Summing Up: Highly recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 52 (5), January, 2015)
“This is an excellent book which can be used for a one- or two-semester upper undergraduate course or first or second year graduate course in transcendental numbers. … There are 28 chapters in 205 pages resulting in an average of 7 pages per chapter. Yet each of these chapters covers a major technique, a major historical development or a major advanced topic.” (Russell Jay Hendel, MAA Reviews, September, 2014)
“The book under review provides an introduction to the fascinating topic of transcendental numbers for senior undergraduate and first-year graduate students. … Each chapter ends with a number of related exercises helping the beginning student develop her/his practical skills. … The utmost lucid and detailed presentation of the material will be very helpful to beginners in the field, who are led from the historical origins of the subject up to the forefront of current research.” (Werner Kleinert, zbMATH, Vol. 1297, 2014)
- Table of contents (28 chapters)
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Liouville’s Theorem
Pages 1-6
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Hermite’s Theorem
Pages 7-9
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Lindemann’s Theorem
Pages 11-14
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The Lindemann–Weierstrass Theorem
Pages 15-18
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The Maximum Modulus Principle and Its Applications
Pages 19-22
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Table of contents (28 chapters)
- Download Preface 1 PDF (238.2 KB)
- Download Sample pages 1 PDF (135 KB)
- Download Table of contents PDF (793.5 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Transcendental Numbers
- Authors
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- M. Ram Murty
- Purusottam Rath
- Copyright
- 2014
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-1-4939-0832-5
- DOI
- 10.1007/978-1-4939-0832-5
- Softcover ISBN
- 978-1-4939-0831-8
- Edition Number
- 1
- Number of Pages
- XIV, 217
- Topics
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