Transcendental Number Theory

Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

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, 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 Sprindžuk'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.