加性数论：经典基

图书标准信息

• 作者 [美]纳森 著
• 出版社 世界图书出版公司
• 出版时间 2012-06
• 版次 1
• ISBN 9787510044090
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 342页
• 原版书名 Additive Number Theory：The Classical Bases(GTM 164)

【内容简介】

　　《加性数论（经典基）》分为上下2卷。堆垒数论讨论的是很经典的直接问题。在这个问题中，首先假定有一个自然数集合a和大于等于2的整数h，定义的和集ha是由所有的h和a中元素乘积的和组成，试图描述和集ha的结构；相反地，在逆问题中，从和集ha开始，去寻找这样的一个集合a。近年来，有关整数有限集的逆问题方面取得了显著进展。特别地，freiman,kneser,pl＆uuml;nnecke,vosper以及一些其他的学者在这方面做出了突出的贡献。本书中包括了这些结果，并且用freiman定理的ruzsa证明将本书的内容推向了高潮。

【目录】

preface
notationandconventior
iwaring'sproblem
1sumsofpolygor
1.1polygonalnumber
1.2lagrange'stheorem
1.3quadraticforms
1.4ternaryquadraticforms
1.5sumsofthreesquares
1.6thinsetsofsquares
1.7thepolygonalnumbertheorem
1.8notes
1.9exercises
2waring'sproblemforcubes
2.1sumsofcubes
2.2thewieferich-kempnertheorem
2.3linnik'stheorem
2.4sumsoftwocubes
2.5notes
.2.6exercises
3thehilbert-waringtheorem
3.1polynomialidentitiesandaconjectureofhurwitz
3.2hermitepolynomialsandhilbert'sidentity
3.3aproofbyinduction
3.4notes
3.5exercises
4weyl'sinequality
4.1tools
4.2differenceoperator
4.3easierwaring'sproblem
4.4fractionalparts
4.5weyl'sinequalityandhua'slemma
4.6notes
4.7exercises
5thehardy-littlewoodasymptoticformula
5.1thecirclemethod
5.2waring'sproblemfork=1
5.3thehardy-littlewooddecomposition
5.4theminorarcs
5.5themajorarcs
5.6thesingularintegral
5.7thesingularseries
5.8conclusion
5.9notes
5.10exercises
iithegoldbachconjecture
6elementaryestimatesforprimes
6.1euclid'stheorem
6.2chebyshev'stheorem
6.3merter'stheorems
6.4brun'smethodandtwinprimes
6.5notes
6.6exercises
7theshnirel'man-goldbachtheorem
7.1thegoldbachconjecture
7.2theselbergsieve
7.3applicatiorofthesieve
7.4shnirel'manderity
7.5theshnirel'man-goldbachtheorem
7.6romanov'stheorem
7.7coveringcongruences
7.8notes
7.9exercises
8sumsofthreeprimes
8.1vinogradov'stheorem
8.2thesingularseries
8.3decompositionintomajorandminorarcs
8.4theintegraloverthemajorarcs
8.5anexponentialsumoverprimes
8.6proofoftheasymptoticformula
8.7notes
8.8exercise
9thelinearsieve
9.1ageneralsieve
9.2cortructionofacombinatorialsieve
9.3approximatior
9.4thejurkat-richerttheorem
9.5differential-differenceequatior
9.6notes
9.7exercises
10chen'stheorem
10.1primesandalmostprimes
10.2weights
10.3prolegomenatosieving
10.4alowerboundfors（a,p,z）
10.5anupperboundfors（aq,p,z）
10.6anupperboundfors（b,p,y）
10.7abilinearforminequality
10.8conclusion
10.9notes
iiiappendix
arithmeticfunctior
a.1theringofarithmeticfunctior
a.2sumsandintegrals
a.3multiplicativefunctior
a.4thedivisorfunction
a.5theeulerφ-function
a.6themobiusfunction
a.7ramanujansums
a.8infiniteproducts
a.9notes
a.10exercises
bibliography
index