Transcendental number theory
Material type:
TextLanguage: English Series: Cambridge mathematical libraryPublication details: Cambridge : Cambridge University Press, 1975. Description: xiv, 169pISBN: 9781009229944Subject(s): Transcendental numbers | Gelfond-Schneider theorem | Lindemann-Weierstrass theorem | Number TheoryDDC classification: 511.46 Online resources: Table of Contents | Index | Reviews Summary: 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.
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"First published 1975. Reprinted with additional material 1979. Reissued as a paperback with updated material in the Cambridge Mathematical Library series 1990. Reprinted with introduction 2022."-- title page verso.
Includes bibliographical references and index.
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.
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