First published in 1975, this classic book gives a systematic account of transcendental number theory, including the author's contributions and their many applications. For this edition, David Masser has written an introduction explaining Baker's achievement in broad strokes, and an afterword listing more recent developments related to Baker's work.
First published in 1975, this classic book gives a systematic account of transcendental number theory, including the author's contributions and their many applications. For this edition, David Masser has written an introduction explaining Baker's achievement in broad strokes, and an afterword listing more recent developments related to Baker's work.
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.
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.
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