ENGLISH

Additive number theory: Inverse problems and the geometry of sumsets

By Melvyn B. Nathanson

Book information

Publisher
Springer
Year
1996
ISBN
9780387946559, 0387946551
LCC
QA241 .N3468 1996
Open Library ID
OL975846M
Language
english
Format
DJVU
Filesize
2 MB (2486397 bytes)
Series
Graduate texts in mathematics 165
Pages
312\312
Library
Kolxo3
DPI
600
Time added
2010-07-29 05:14:56

Description

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, Plünnecke, 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.

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