Metric Number Theory

Hardcover | July 1, 1998

byGlyn Harman

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This book deals with the number-theoretic properties of almost all real numbers. It brings together many different types of result never covered within the same volume before, thus showing interactions and common ideas between different branches of the subject. It provides an indispensablecompendium of basic results, important theorems and open problems. Starting from the classical results of Borel, Khintchine and Weyl, normal numbers, Diophantine approximation and uniform distribution are all discussed. Questions are generalized to higher dimensions and various non-periodic problemsare also considered (for example restricting approximation to fractions with prime numerator and denominator). Finally, the dimensions of some of the exceptional sets of measure zero are considered.

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This book deals with the number-theoretic properties of almost all real numbers. It brings together many different types of result never covered within the same volume before, thus showing interactions and common ideas between different branches of the subject. It provides an indispensablecompendium of basic results, important theorems...

Professor G. Harman, School of Mathematics, Mathematics Institute, University of Wales Cardiff, Senghennydd Road, Cardiff, CF2 4YH, email: Harman@cf.ac.uk
Format:HardcoverDimensions:316 pages, 9.21 × 6.14 × 0.83 inPublished:July 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198500831

ISBN - 13:9780198500834

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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