This is a systematic account of the multiplicative structure of integers, from the probabilistic point of view. The authors are especially concerned with the distribution of the divisors, which is as fundamental and important as the additive structure of the integers, and yet until now has hardly been discussed outside of the research literature. Hardy and Ramanujan initiated this area of research and it was developed by Erdös in the thirties. His work led to some deep and basic conjectures of wide application which have now essentially been settled. This book contains detailed proofs, some of which have never appeared in print before, of those conjectures that are concerned with the propinquity of divisors. Consequently it will be essential reading for all researchers in analytic number theory.

Divisors (Cambridge Tracts in Mathematics, Series Number 90)

Science & Math

TENENBAUM, Gérald

Hall, Richard R.

Mathematics

Cambridge University Press

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.

Sets of Multiples (Cambridge Tracts in Mathematics, Series Number 118)

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Books by Hall, Richard R.

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Divisors (Cambridge Tracts in Mathematics, Series Number 90)

Sets of Multiples (Cambridge Tracts in Mathematics, Series Number 118)

Divisors (Cambridge Tracts in Mathematics, Series Number 90)

Sets of Multiples (Cambridge Tracts in Mathematics, Series Number 118)