Sets of Multiples

Research monograph in analytic and probabilistic number theory.

Richard R. Hall (Author)

9780521404242, Cambridge University Press

Hardback, published 10 October 1996

284 pages
23.6 x 16 x 2.1 cm, 0.532 kg

"This book...should make a useful addition to the libraries of those interested in this general subject area." G. Greaves, Mathematical Reviews

The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of Sequences by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. The author sets out to give a coherent, essentially self-contained account of the existing theory and at the same time to bring the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, as well as several branches of number theory. This Tract is the first devoted to the subject, and will be of value to research workers or graduate students in number theory.

Preface
Introduction
Notation
First ideas
1. Besicovitch and Behrend sequences
2. Derived sequences and densities
3. Oscillation
4. Probabilistic group theory
5. Divisor density
6. Divisor uniform distribution
7. H(x,y,z)
Bibliography
Index.

Subject Areas: Number theory [PBH]