Search Results for transcendental-number-theory

A systematic account of transcendental number theory, or those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. First published in 1975 and revised in 1979.

Author: Alan Baker

Publisher: Cambridge University Press

ISBN: 052139791X

Category: Mathematics

Page: 165

View: 265

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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.
1990-09-28 By Alan Baker

This book is a survey of the most important directions of research in transcendental number theory.

Author: A.N. Parshin

Publisher: Springer Science & Business Media

ISBN: 9783662036440

Category: Mathematics

Page: 345

View: 452

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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.
2013-03-09 By A.N. Parshin

This book is a survey of the most important directions of research in transcendental number theory.

Author: A.N. Parshin

Publisher: Springer

ISBN: 3642082599

Category: Mathematics

Page: 345

View: 854

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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.
2010-12-08 By A.N. Parshin

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students.

Author: Edward B. Burger

Publisher: Springer Science & Business Media

ISBN: 0387214445

Category: Mathematics

Page: 263

View: 416

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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.
2004-07-28 By Edward B. Burger

This book is a survey of the most important directions of research in transcendental number theory.

Author: A.N. Parshin

Publisher: Springer

ISBN: 3540614672

Category: Mathematics

Page: 345

View: 835

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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.
1997-10-06 By A.N. Parshin

This volume consists of a collection of papers devoted primarily to transcendental number theory and diophantine approximations written by the author.

Author: Gregory Chudnovsky

Publisher: American Mathematical Soc.

ISBN: 9780821815007

Category: Mathematics

Page: 450

View: 744

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This volume consists of a collection of papers devoted primarily to transcendental number theory and diophantine approximations written by the author. Most of the materials included in this volume are English translations of the author's Russian manuscripts, extensively rewritten and brought entirely up to date. These papers and other papers included in this volume were available to specialists in manuscript form, but this is the first time that they have been collected and published.Though the earlier papers have been preserved in the form in which they were prepared initially, the volume is organized in such a way as to reflect recent progress and to allow readers to follow recent developments in the field. As an introductory guide to the volume, the author included an expanded and updated text of his invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki. The appendix contains a paper on the extremality of certain multidimensional manifolds prepared by A. I. Vinogradov and the author in 1976. Chudnovsky received a MacArthur Foundation Fellowship in 1981.

The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.

Author: Carl Ludwig Siegel

Publisher: Princeton University Press

ISBN: 9781400882359

Category: Mathematics

Page: 102

View: 797

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The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.
2016-03-02 By Carl Ludwig Siegel

Author:

Publisher:

ISBN: UOM:39015051616871

Category: Numbers, Transcendental

Page: 159

View: 175

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1998 By

Author: A. Bijlsma

Publisher:

ISBN: UOM:39015017316004

Category: Transcendental numbers

Page: 101

View: 401

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1978 By A. Bijlsma

This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications.

Author: Saradha Natarajan

Publisher: Springer Nature

ISBN: 9789811541551

Category: Mathematics

Page: 174

View: 511

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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.
2020-05-02 By Saradha Natarajan

Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory. This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students.

Author: M. Ram Murty

Publisher: Springer

ISBN: 9781493908325

Category: Mathematics

Page: 217

View: 115

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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.
2014-06-24 By M. Ram Murty

The text also chronicles the historical development of the theory's methods and explores the connections with other problems in number theory.

Author: A. O. Gelfond

Publisher: Courier Dover Publications

ISBN: 9780486802251

Category: Mathematics

Page: 208

View: 105

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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.
2015-01-05 By A. O. Gelfond

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students.

Author: Edward B. Burger

Publisher:

ISBN: 1475741154

Category:

Page: 278

View: 869

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2014-01-15 By Edward B. Burger

This work deals with recent progress in current aspects of number theory and covers a wide variety of topics.

Author: Michel Waldschmidt

Publisher: American Mathematical Soc.

ISBN: 9780821806067

Category: Mathematics

Page: 399

View: 648

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To observe the tenth anniversary of the founding of the Ramanujan Mathematical Society, an international conference on Discrete Mathematics and Number Theory was held in January 1996 in Tiruchirapalli, India. This volume contains proceedings from the number theory component of that conference. Papers are divided into four groups: arithmetic algebraic geometry, automorphic forms, elementary and analytic number theory, and transcendental number theory. This work deals with recent progress in current aspects of number theory and covers a wide variety of topics.

Three major branches of number theory are included in the volume: namely analytic number theory, algebraic number theory, and transcendental number theory.

Author: Kağan Kurşungöz

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110761191

Category: Mathematics

Page: 140

View: 406

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Three major branches of number theory are included in the volume: namely analytic number theory, algebraic number theory, and transcendental number theory. Original research is presented that discusses modern techniques and survey papers from selected academic scholars.
2021-12-20 By Kağan Kurşungöz

Author:

Publisher:

ISBN: 3540533869

Category:

Page:

View: 200

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1991 By

The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central.

Author: Ivan Niven

Publisher: Cambridge University Press

ISBN: 0883850389

Category: Mathematics

Page: 164

View: 141

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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 technique. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central. Well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There are notes at the end of each chapter citing the main sources used by the author and suggesting further reading.
2005-08-18 By Ivan Niven

Author: Baker

Publisher:

ISBN: OCLC:249197016

Category:

Page:

View: 953

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1994 By Baker

Translated from the Russian edition of 1987, this is a model of elegant, crisp legibility in math printing. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Author: Andrej Borisovič Šidlovskij

Publisher: Walter de Gruyter

ISBN: 3110115689

Category: Number theory

Page: 466

View: 898

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Shidlovskii (mechanics and math, Moscow State U.) is concerned here with an important direction of research in the theory of transcendental numbers, the so-called E-functions. He gives a detailed discussion on applications of the Siegel-Shidlovskii method for proving transcendence and algebraic independence results for E- functions. Translated from the Russian edition of 1987, this is a model of elegant, crisp legibility in math printing. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory.

Author: Michel Planat

Publisher: MDPI

ISBN: 9783039366866

Category: Computers

Page: 206

View: 880

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According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.
2021-01-20 By Michel Planat