Alan Baker

Transcendental Number Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 9. Juni 2022
• Englisch
• ISBN-13: 9781009229968
• Artikelnr.: 66177587

Autorenporträt

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.

Inhaltsangabe

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.