Metric Number Theory

Erscheinungsjahr 1998
ISBN: 978-0-19-850083-4
Verlag: OUP Oxford

Buch, Englisch, 316 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 640 g

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 indispensable compendium 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 problems are 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.

Autoren/Hrsg.

Harman, G.

Harman, Glyn

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

- Introduction

- 1: Normal numbers

- 2: Diophantine approximation

- 3: GCD sums with applications

- 4: Schmidt's method

- 5: Uniform distribution

- 6: Diophantine approximation with restricted numerator and denominator

- 7: Non-integer sequences

- 8: The integer parts of sequences

- 9: Diophantine approximation on manifolds

- 10: Hausdorff dimension of exceptional sets

- References

- Index

Über Autor(innen)

Professor G. Harman, School of Mathematics, Mathematics Institute, University of Wales Cardiff, Senghennydd Road, Cardiff, CF2 4YH, email: [e-mail]