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.

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.

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.

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.

Introduction to Algebraic Independence Theory
Introduction to Algebraic Independence Theory

Author: Yuri V. Nesterenko

Publisher: Springer

Published: 2003-07-01

Total Pages: 257

ISBN-13: 3540445501

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In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.

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.

Transcendental Number Theory
Transcendental Number Theory

Author: Alan Baker

Publisher: Cambridge University Press

Published: 1990-09-28

Total Pages: 180

ISBN-13: 9780521397919

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First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.

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.

Making Transcendence Transparent
Making Transcendence Transparent

Author: Edward B. Burger

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 266

ISBN-13: 1475741146

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This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.