Sets of Multiples

ISBN-13: 9780521404242 / Angielski / Twarda / 1996 / 284 str.

Richard R. Hall; R. R. Hall

Opis

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.

Recenzje

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

Spis treści

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.