"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap) "In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull. LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap) In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approximations to algebraic numbers. The present volume is an expanded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field (Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. . . . this book is highly recommended" (Mededelingen van het Wiskundig Genootschap) Front Matter....Pages I-XII Approximation to Irrational Numbers by Rationals....Pages 1-26 Simultaneous Approximation....Pages 27-47 Games and Measures....Pages 48-79 Integer Points in Parallelepipeds....Pages 80-113 Roth’s Theorem....Pages 114-150 Simultaneous Approximation to Algebraic Numbers....Pages 151-207 Norm Form Equations....Pages 208-250 Approximation By Algebraic Numbers....Pages 251-288 Back Matter....Pages 289-299 In 1970, at the University of Colorado, the author delivered a course of lectures on his famous generalization, relating to Roth's theorem on rational approxi- mations to algebraic numbers. This volume is a version of the original mimeographed notes on the course.
