Additive Number Theory: Inverse Problems and the Geometry of Sumsets
by Melvyn B Nathanson (9780387946559)

Additive Number Theory: Inverse Problems and the Geometry of Sumsets
 
Melvyn B Nathanson
Release Date: 01 August 1996
Format: Hardback
Pages: 296
Category: Number Theory
ISBN: 9780387946559
ISBN-10: 0387946551



Many classical problems in additive number theory are direct problems, in which one starts with a set "A" of natural numbers and an integer "H -> 2," and tries to describe the structure of the sumset "hA" consisting of all sums of "h" elements of "A," By contrast, in an inverse problem, one starts with a sumset "hA," and attempts to describe the structure of the underlying set "A," In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, PlA1/4nnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an "n"-dimensional arithmetic progression.

AUD $140.95

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