Metric Number Theory - Glyn Harman

Metric Number Theory

(Autor)

Buch | Hardcover
316 Seiten
1998
Oxford University Press (Verlag)
978-0-19-850083-4 (ISBN)
329,95 inkl. MwSt
This book deals with the arithmetical properties of almost all real numbers. It brings together many different types of result (including normal numbers, Diophantine approximation and uniform distribution) never covered within the same volume before. By this approach interactions and common themes between different branches of the subject are revealed.
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.

Professor G. Harman, School of Mathematics, Mathematics Institute, University of Wales Cardiff, Senghennydd Road, Cardiff, CF2 4YH, email: Harman@cf.ac.uk

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

Erscheint lt. Verlag 1.10.1998
Reihe/Serie London Mathematical Society Monographs ; 18
Verlagsort Oxford
Sprache englisch
Maße 162 x 242 mm
Gewicht 619 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
ISBN-10 0-19-850083-1 / 0198500831
ISBN-13 978-0-19-850083-4 / 9780198500834
Zustand Neuware
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