Additive number theory : inverse problems and the geometry of sumsets

＜図書＞
Additive number theory : inverse problems and the geometry of sumsets

責任表示	Melvyn B. Nathanson
シリーズ	Graduate texts in mathematics ; 165
データ種別	図書
出版情報	New York ; Tokyo : Springer , c1996
本文言語	英語
大きさ	xiv, 293 p. : ill. ; 25 cm
概要	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, Pl nnecke, 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. 続きを見る

一般注記	Includes bibliographical reference(p.[283]-291) and index
著者標目	*Nathanson, Melvyn Bernard, 1944-
件　名	LCSH:Number theory
分　類	LCC:QA241 DC20:512/.73 NDC8:412.3 NDC8:410.7
書誌ID	1000924018
ISBN	0387946551
NCID	BA28326766
巻冊次	ISBN:0387946551
登録日	2009.09.16
更新日	2009.11.02