Diophantine Approximation

✍ Scribed by Wolfgang M. Schmidt (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1980
• Tongue: English
• Leaves: 311
• Series: Lecture Notes in Mathematics 785
• Edition: 1
• Category: Library

✦ Synopsis

"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)

✦ Table of Contents

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

✦ Subjects

Number Theory