算术教程

图书标准信息

• 作者 [法]赛瑞 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510005350
• 定价 19.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 115页
• 正文语种 英语
• 原版书名 A Course in Arithmetic

【内容简介】

Thefirstoneispurelyalgebraic.Itsobjectiveistheclassificationofquadraticformsoverthefieldofrationalnumbers（Hasse-Minkowskitheorem）.ItisachievedinChapterIV.Thefirstthreechapterscontainsomepreliminaries：quadraticreciprocitylaw，p-adicfields，Hilbertsymbols.ChapterVappliestheprecedingresultstointegralquadraticformsindiscriminant+1.Theseformsoccurinvariousquestions：modularfunctions，differentialtopology，finitegroups.Thesecondpart（ChaptersVIandVII）uses"analytic"methods（holomor-phicfunctions）.ChapterVIgivestheproofofthe"theoremonarithmeticprogressions"duetoDirichlet;thistheoremisusedatacriticalpointinthefirstpart（Chapter111，no.2.2）.ChapterVIIdealswithmodularforms，andinparticular，withthetafunctions.SomeofthequadraticformsofChapterVreappearhere.

【作者简介】

J.–P. SERRE，法国著名数学家。是迄今为止获得“数学界诺贝尔奖”的菲尔兹奖的年轻的得主。

【目录】

Preface
PartI-AlgebraicMethods
ChapterIFinitefields
1-Generalities
2-Equationsoverafinitefield
3-Quadraticreciprocitylaw
Appendix-Anotherproofofthequadraticreciprocitylaw
ChapterIIp-adicfields
1-TheringZpandthefield
2-p-adicequations
3-Themultiplicativegroupof
ChapterIInHilbertsymbol
1-Localproperties
2-Globalproperties
ChapterIVQuadraticformsoverQpandoverQ
1-Quadraticforms
2-QuadraticformsoverQ
3-QuadraticformsoverQ
AppendixSumsofthreesquares
ChapterVIntegralquadraticformswithdiscriminant
1-Preliminaries
2-Statementofresults
3-Proofs
PartII-AnalyticMethods
ChapterVI-Thetheoremonarithmeticprogressions
1-Charactersoffiniteabeliangroups
2-Dirichletseries
3-ZetafunctionandLfunctions
4-DensityandDirichlettheorem
ChapterVll-Modularforms
1-Themodulargroup
2-Modularfunctions
3-Thespaceofmodularforms
4-Expansionsatinfinity
5-Heckeoperators
6-Thetafunctions
Bibliography
IndexofDefinitions
IndexofNotations