Transcendental And Algebraic Numbers

Author : A. O. Gelfond
Publisher : Courier Dover Publications
Page : 208 pages
File Size : 50,7 Mb
Release : 2015-01-05
Category : Mathematics
ISBN : 9780486802251

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Transcendental and Algebraic Numbers by A. O. Gelfond Pdf

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.

Author : Alan Baker
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,5 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009229968

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Transcendental Number Theory by Alan Baker Pdf

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.

Author : M. Ram Murty,Purusottam Rath
Publisher : Springer
Page : 219 pages
File Size : 55,6 Mb
Release : 2014-06-24
Category : Mathematics
ISBN : 9781493908325

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Transcendental Numbers by M. Ram Murty,Purusottam Rath Pdf

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.

Author : Alan Baker
Publisher : Cambridge University Press
Page : 185 pages
File Size : 55,5 Mb
Release : 2022-06-09
Category : Computers
ISBN : 9781009229944

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Transcendental Number Theory by Alan Baker Pdf

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

Author : Serge Lang
Publisher : Unknown
Page : 120 pages
File Size : 40,6 Mb
Release : 1966
Category : Transcendental numbers
ISBN : STANFORD:36105031201903

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Introduction to Transcendental Numbers by Serge Lang Pdf

Author : A. O. Gelfond
Publisher : Unknown
Page : 190 pages
File Size : 44,8 Mb
Release : 1960
Category : Electronic
ISBN : OCLC:488619863

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Transcendental and Algebraic Numbers by A. O. Gelfond Pdf

Author : Harry Pollard,Harold G. Diamond
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 49,7 Mb
Release : 1975-12-31
Category : Algebraic number theory
ISBN : 9781614440093

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The Theory of Algebraic Numbers: Second Edition by Harry Pollard,Harold G. Diamond Pdf

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.

Author : Yann Bugeaud
Publisher : Cambridge University Press
Page : 317 pages
File Size : 47,6 Mb
Release : 2012-07-05
Category : Mathematics
ISBN : 9780521111690

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Distribution Modulo One and Diophantine Approximation by Yann Bugeaud Pdf

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.

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 53,7 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Author : Andrei B. Shidlovskii
Publisher : Walter de Gruyter
Page : 489 pages
File Size : 49,9 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 9783110889055

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Transcendental Numbers by Andrei B. Shidlovskii Pdf

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.

Author : K. Mahler
Publisher : Springer
Page : 274 pages
File Size : 43,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540379812

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Lectures on Transcendental Numbers by K. Mahler Pdf

Author : A.N. Parshin,I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662036440

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Number Theory IV by A.N. Parshin,I.R. Shafarevich Pdf

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.

Author : Gregory Chudnovsky
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 53,7 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821815007

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Contributions to the Theory of Transcendental Numbers by Gregory Chudnovsky Pdf

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.

Author : Ivan Niven
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 46,5 Mb
Release : 1985-12-31
Category : Irrational numbers
ISBN : 9781614440116

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Irrational Numbers by Ivan Niven Pdf

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.

Author : Clifford A. Pickover
Publisher : Oxford University Press
Page : 420 pages
File Size : 43,7 Mb
Release : 2003-01-16
Category : Mathematics
ISBN : 0195348001

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Wonders of Numbers by Clifford A. Pickover Pdf

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.