Transcendental Numbers
Transcendental Numbers

Author: M. Ram Murty

Publisher: Springer

Published: 2014-06-24

Total Pages: 219

ISBN-13: 1493908324

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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.

Transcendental Number Theory
Transcendental Number Theory

Author: Alan Baker

Publisher: Cambridge University Press

Published: 2022-06-09

Total Pages: 185

ISBN-13: 100922994X

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Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

Transcendental Numbers. (AM-16)
Transcendental Numbers. (AM-16)

Author: Carl Ludwig Siegel

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 102

ISBN-13: 1400882354

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The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.

Number Theory IV
Number Theory IV

Author: A.N. Parshin

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 351

ISBN-13: 3662036444

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This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.

Transcendental Numbers
Transcendental Numbers

Author: Andrei B. Shidlovskii

Publisher: Walter de Gruyter

Published: 2011-06-01

Total Pages: 489

ISBN-13: 3110889056

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Wonders of Numbers
Wonders of Numbers

Author: Clifford A. Pickover

Publisher: Oxford University Press

Published: 2003-01-16

Total Pages: 420

ISBN-13: 9780195348002

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Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will enchant even the most left-brained of readers. Hosted by the quirky Dr. Googol--who resides on a remote island and occasionally collaborates with Clifford Pickover--Wonders of Numbers focuses on creativity and the delight of discovery. Here is a potpourri of common and unusual number theory problems of varying difficulty--each presented in brief chapters that convey to readers the essence of the problem rather than its extraneous history. Peppered throughout with illustrations that clarify the problems, Wonders of Numbers also includes fascinating "math gossip." How would we use numbers to communicate with aliens? Check out Chapter 30. Did you know that there is a Numerical Obsessive-Compulsive Disorder? You'll find it in Chapter 45. From the beautiful formula of India's most famous mathematician to the Leviathan number so big it makes a trillion look small, Dr. Googol's witty and straightforward approach to numbers will entice students, educators, and scientists alike to pick up a pencil and work a problem.

Irrationality and Transcendence in Number Theory
Irrationality and Transcendence in Number Theory

Author: David Angell

Publisher: CRC Press

Published: 2021-12-30

Total Pages: 243

ISBN-13: 100052373X

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Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation. Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates. Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background.

Pillars of Transcendental Number Theory
Pillars of Transcendental Number Theory

Author: Saradha Natarajan

Publisher: Springer Nature

Published: 2020-05-02

Total Pages: 184

ISBN-13: 9811541558

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This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite–Lindemann–Weierstrass theorem, Gelfond–Schneider theorem, Schmidt’s subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker’s original results. This book presents Baker’s original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of “Exercises” and interesting information presented as “Notes,” intended to spark readers’ curiosity.

Transcendental and Algebraic Numbers
Transcendental and Algebraic Numbers

Author: A. O. Gelfond

Publisher: Courier Dover Publications

Published: 2015-01-05

Total Pages: 212

ISBN-13: 0486802256

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Primarily an advanced study of the modern theory of transcendental and algebraic numbers, this treatment by a distinguished Soviet mathematician focuses on the theory's fundamental methods. The text also chronicles the historical development of the theory's methods and explores the connections with other problems in number theory. The problem of approximating algebraic numbers is also studied as a case in the theory of transcendental numbers. Topics include the Thue-Siegel theorem, the Hermite-Lindemann theorem on the transcendency of the exponential function, and the work of C. Siegel on the transcendency of the Bessel functions and of the solutions of other differential equations. The final chapter considers the Gelfond-Schneider theorem on the transcendency of alpha to the power beta. Each proof is prefaced by a brief discussion of its scheme, which provides a helpful guide to understanding the proof's progression.

Contributions to the Theory of Transcendental Numbers
Contributions to the Theory of Transcendental Numbers

Author: Gregory Chudnovsky

Publisher: American Mathematical Soc.

Published: 1984

Total Pages: 464

ISBN-13: 0821815008

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Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.