算术教程 (英文 影印版)
算术教程/ A Course in Arithmetic
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九品
仅1件
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
装帧平装
货号57
上书时间2020-06-12
商品详情
- 品相描述:九品
图书标准信息
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作者
[法]赛瑞 著
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出版社
世界图书出版公司
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出版时间
2009-08
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版次
1
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ISBN
9787510005350
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定价
19.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
115页
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正文语种
英语
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原版书名
A Course in Arithmetic
- 【内容简介】
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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.
- 【目录】
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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
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