Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Approximation by Algebraic Numbers written by Yann Bugeaud and published by Cambridge University Press. This book was released on 2004-11-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and broad account of the approximation and classification of real numbers suited for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the comprehensive list of more than 600 references.

Download or read book Transcendental and Algebraic Numbers written by A. O. Gelfond and published by Courier Dover Publications. This book was released on 2015-01-05 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Approximation of Algebraic Numbers by Algebraic Numbers and the Theory of Transcendental Numbers written by Aleksandr Osipovich Gelʹfond and published by . This book was released on 1952 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Distribution Modulo One and Diophantine Approximation written by Yann Bugeaud and published by Cambridge University Press. This book was released on 2012-07-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.

Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

Download or read book Contributions to the Theory of Transcendental Numbers written by Gregory Chudnovsky and published by American Mathematical Soc.. This book was released on 1984 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Theory of Algebraic Numbers Second Edition written by Harry Pollard and published by American Mathematical Soc.. This book was released on 1975-12-31 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.

Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Download or read book Number Theory IV written by A.N. Parshin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Diophantine Approximation on Linear Algebraic Groups written by Michel Waldschmidt and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

Download or read book Simultaneous Approximations in Transcendental Number Theory written by A. Bijlsma and published by . This book was released on 1978 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Irrational Numbers written by Ivan Niven and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book First Order Categorical Logic written by M. Makkai and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Classical Theory of Algebraic Numbers written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.

Download or read book Transcendental Numbers written by Andrei B. Shidlovskii and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Irrationality and Transcendence in Number Theory written by David Angell and published by CRC Press. This book was released on 2021-12-30 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.