Divisors

This is a systematic account of the multiplicative structure of integers, from the probabilistic point of view.

Richard R. Hall (Author), Gérald Tenenbaum (Author)

9780521091671, Cambridge University Press

Paperback / softback, published 4 December 2008

184 pages
22.9 x 15.2 x 1.1 cm, 0.28 kg

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.

1. Preliminaries
2. The Normal Distribution of the Prime Factors
3. Sieving by an Interval
4. Imaginary Powers
5. Measures of Propinquity
6. Erdös' Conjecture
7. Hooley's ?r-functions - Sharp Bounds
8. Hooley's ?r-functions - the Critical Interval.

Subject Areas: Number theory [PBH]