Transcendental And Algebraic Numbers
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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.
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 And Algebraic Numbers
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Author : A. O. Gelfond
language : en
Publisher:
Release Date : 1960
Transcendental And Algebraic Numbers written by A. O. Gelfond and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.
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.
Introduction To Transcendental Numbers
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Author : Serge Lang
language : en
Publisher:
Release Date : 1966
Introduction To Transcendental Numbers written by Serge Lang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Transcendental numbers categories.
Contributions To The Theory Of Transcendental Numbers
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Author : Gregory Chudnovsky
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Contributions To The Theory Of Transcendental Numbers written by Gregory Chudnovsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Numbers, Transcendental categories.
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.
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.
Lectures On Transcendental Numbers
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Author : K. Mahler
language : en
Publisher: Springer
Release Date : 2006-11-14
Lectures On Transcendental Numbers written by K. Mahler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Irrational Numbers
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Author : Ivan Niven
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-12-31
Irrational Numbers written by Ivan Niven and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-31 with Irrational numbers categories.
In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary techniques. The last third of the monograph treats normal and transcendental numbers, including the transcendence of p and its generalization in the Lindermann theorem, and the Gelfond-Schneider theorem. Most of the material in the first two thirds of the book presupposes only calculus and beginning number theory. The book is almost wholly self-contained. The results needed from analysis and algebra are central and well-known theorems, and complete references to standard works are given to help the beginner. The chapters are, for the most part, independent. There is a set of notes at the end of each chapter citing the main sources used by the author and suggesting further reading.