椭圆曲线和模型式引论（第2版）（英文版）

图书标准信息

• 作者 N.Koblitz 著
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 2
• ISBN 9787506260145
• 定价 27.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 248页

【内容简介】

Mypurposeistomakethesubjectaccessibletothosewhofindithardtoreadmoreadvancedormorealgebraicallyorientedtreatments.AtthesametimeIwanttointroducetopicswhichareattheforefrontofcurrentresearch.Down-to-earthexamplesaregiveninthetextandexercises，withtheaimofmakingthematerialreadableandinterestingtomathematiciansinfieldsfarremovedfromthesubjectofthebook.

【目录】

PrefacetotheFirstEdition
PrefacetotheSecondEdition
CHAPTERIFromCongruentNumberstoEllipticCurves
1.Congruentnumbers
2.Acertaincubicequation
3.Ellipticcurves
4.Doublyperiodicfunctions
5.Thefieldofellipticfunctions
6.EllipticcurvesinWeierstrassform
7.Theadditionclaw
8.Pointsoffiniteorder
9.Pointsoverfinitefields,andthecongruentnumberproblem

CHAPTERIITheHasse-WeilL-FunctionofanEllipticCurve
I.Thecongruencezeta-function
2.Thezeta-functionofE
3.Varyingtheprimep
4.Theprototype:theRiemannzeta-function
5.TheHasse-WeilL-functionanditsfunctionalequation
6.Thecriticalvalue

CHAPTERIIIModularforms
1.SL2(Z)anditscongruencesubgroups
2.ModularformsforSL2(Z)
3.Modularformsforcongruencesubgroups
4.Transformationformulaforthetheta-function
5.Themodularinterpretation,andHeckeoperators

CHAPTERIVModularFormsofHalfIntegerWeight
1.Definitionsandexamples
2.Eisensteinseriesofhalfintegerweightfor(4)
3.Heckeoperatorsonformsofhalfintegerweight
4.ThetheoremsofShimura,Waldspurger,Tunnell,andthecongruentnumberproblem
Answers,Hints,andReferenesforSelectedExercises
Bibliography
Index