Metric Number Theory

by Glyn Harman

Overview

This book examines the number-theoretic properties of the real numbers. It collects a variety of new ideas and develops connections between different branches of mathematics. An indispensable compendium of basic results, the text also includes important theorems and open problems. The book begins with the classical results of Borel, Khintchine, and Weyl, and then proceeds to Diophantine approximation, GCD sums, Schmidt's method, and uniform distribution. Other topics include generalizations to higher dimensions and various non-periodic problems (for example, restricting approximation to fractions with prime numerator and denominator). It concludes with a chapter on Hausdorf dimensions for exceptional sets of measure zero.

Product Details

ISBN-13:	9780198500834
Publisher:	Oxford University Press
Publication date:	08/13/1998
Series:	London Mathematical Society Monographs , #18
Pages:	316
Product dimensions:	6.10(w) x 9.30(h) x 0.80(d)

About the Author

University of Wales, Cardiff

Table of Contents

Introduction1. Normal numbers2. Diophantine approximation3. GCD sums with applications4. Schmidt's method5. Uniform distribution6. Diophantine approximation with restricted numerator and denominator7. Non-integer sequences8. The integer parts of sequences9. Diophantine approximation on manifolds10. Hausdorff dimension of exceptional setsReferencesIndex

Editorial Reviews

"This is an ideal introduction to the subject, with modest prerequisites in analysis and number theory." - Mathematical Reviews

From the Publisher