Transcendental number theory
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Bibliographic Information
Transcendental number theory
（Cambridge mathematical library）
Cambridge University Press, 2022, c1975
- : pbk
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"Reprinted with introduction 2022"--T.p. verso
Original papers: p. 130-144
Further publications: p. 145-154
Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
- 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.
by "Nielsen BookData"
