Sets of Multiples [Paperback]

Research monograph in analytic and probabilistic number theory.The theory of sets of mutliples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development in recent years. 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.This Tract is the first devoted to the subject, and will be of value to number theorists, whether they be research workers or graduate students.The theory of sets of mutliples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development in recent years. 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.This Tract is the first devoted to the subject, and will be of value to number theorists, whether they be research workers or graduate students.The theory of sets of multiples, a subject that 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. In this book, the author gives a coherent, self-contained account of the existing theory, bringing 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, and several branches of number theory.Preface; Introduction; Notation; First ideas; 1. Besicovitch and Behrend sequences; 2. Derived sequences and densities; 3lÅ