Transcendental Number Theory

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.

'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

• 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.