Transcendental Mathematics
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Transcendental Numbers
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Author : M. Ram Murty
language : en
Publisher: Springer
Release Date : 2014-06-24
Transcendental Numbers written by M. Ram Murty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-24 with Mathematics categories.
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
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Author : Alan Baker
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Transcendental Number Theory written by Alan Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Computers categories.
Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.
Transcendental And Algebraic Numbers
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Author : A. O. Gelfond
language : en
Publisher: Courier Dover Publications
Release Date : 2015-01-05
Transcendental And Algebraic Numbers written by A. O. Gelfond and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-05 with Mathematics categories.
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.
Transcendental Number Theory
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Author : Alan Baker
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Transcendental Number Theory written by Alan Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.
Making Transcendence Transparent
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Author : Edward B. Burger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Making Transcendence Transparent written by Edward B. Burger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Transcendental Numbers
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Author : Andrei B. Shidlovskii
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-01
Transcendental Numbers written by Andrei B. Shidlovskii and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.
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.
Number Theory Iv
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Author : A.N. Parshin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Number Theory Iv written by A.N. Parshin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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 Am 16
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Author : Carl Ludwig Siegel
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Transcendental Numbers Am 16 written by Carl Ludwig Siegel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.
Pillars Of Transcendental Number Theory
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Author : Saradha Natarajan
language : en
Publisher: Springer Nature
Release Date : 2020-05-02
Pillars Of Transcendental Number Theory written by Saradha Natarajan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-02 with Mathematics categories.
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.
Number Theory Iv
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Author : A.N. Parshin
language : en
Publisher: Springer
Release Date : 1997-10-06
Number Theory Iv written by A.N. Parshin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-06 with Mathematics categories.
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.