Transcendental Number Theory

Alan Baker, David Masser (Universitat Basel, Switzerland)

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English

Cambridge University Press
09 June 2022

Number theory; Algorithms & data structures

Series: Cambridge Mathematical Library

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 Sprindzuk'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.

By: Alan Baker
Foreword by: David Masser (Universitat Basel Switzerland)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: Revised edition
Dimensions: Height: 228mm, Width: 151mm, Spine: 11mm
Weight: 290g
ISBN: 9781009229944
ISBN 10: 100922994X
Series: Cambridge Mathematical Library
Pages: 190
Publication Date: 09 June 2022
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

Introduction David Masser; Preface; 1. The origins; 2. Linear forms in logarithms; 3. Lower bounds for linear forms; 4. Diophantine equations; 5. Class numbers of imaginary quadratic fields; 6. Elliptic functions; 7. Rational approximations to algebraic numbers; 8. Mahler's classification; 9. Metrical theory; 10. The exponential function; 11. The Shiegel-Shidlovsky theorems; 12. Algebraic independence; Bibliography; Original papers; Further publications; New developments; Some Developments since 1990 David Masser; Index.

Alan Baker was one of the leading British mathematicians of the past century. He took great strides in number theory by, among other achievements, obtaining a vast generalization of the Gelfond-Schneider Theorem and using it to give effective solutions to a large class of Diophantine problems. This work kicked off a new era in transcendental number theory and won Baker the Fields Medal in 1970. David Masser is Professor Emeritus in the Department of Mathematics and Computer Science at the University of Basel. He is a leading researcher in transcendence methods and applications and helped correct the proofs of the original edition of Transcendental Number Theory as Baker's student.

Reviews for Transcendental Number Theory

'Baker's book is the book on transcendental numbers. He covers a majority of those areas that have reached definitive results, presents most of the proofs in a complete yet far more compact form than hitherto available, and covers historical and bibliographical matters with great thoroughness and impeccable scholarship. As literature, it compares well with the finest works of Landau, Rademacher, and Titchmarsh.' Kenneth B. Stolarsky, Bulletin of the American Mathematical Society