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Informationen zum Autor Alan K. Baker was born in Birmingham, UK in 1964. After graduating from the University of Reading in 1991, he endured a series of increasingly unpleasant jobs, culminating in a nine-month stint as a meat-packer in a Sheffield sausage factory, which served to increase his fascination with the macabre and outlandish. Since 1997, he has published a number of books on the paranormal and popular history, which have been translated into seven languages. Klappentext First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics.Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue -- Siegel -- Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindzuk's solution to the Mahler conjecture. Zusammenfassung This classic book gives a systematic account of transcendental number theory! that is numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. The updated volume includes new advances in the theory and many new references. Inhaltsverzeichnis 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 Siegel-Shidlovsky theorems; 12. Algebraic independence; Bibliography; Original papers; Further publications; New developments; Index.
