橢圓曲線和模形式引論

CHAPTERI
FromCongruentNumberstoEllipticCurves
1.Congruentnumbers
2.Acertaincubicequation
3.Ellipticcurves
4.Doublyperiodicfunctions
5.Thefieldofellipticfunctions
6.EllipticcurvesinWeierstrassform
7.Theadditionlaw
8.Pointsoffiniteorder
9.Pointsoverfinitefields,andthecongruentnumberproblem
CHAFFERII
TheHasse-WeilL-FunctionofanEllipticCurve
1.Thecongruencezeta-function
2.Thezeta-functionofEn
3.Varyingtheprimep
4.Theprototype:theRiemannzeta-function
5.TheHasse-WeilL-functionanditsfunctionalequation
6.Thecriticalvalue
CHAFFERIII
Modularforms
1.SL2(Z)anditscongruencesubgroups
2.ModularformsforSL2(Z)
3.Modularformsforcongruencesubgroups
4.Transformationformulaforthetheta-function
5.Themodularinterpretation,andHeckeoperators
CHAPTERIV
ModularFormsofHalfIntegerWeight
1.Definitionsandexamples
2.Eisensteinseriesofhalfintegerweightforto(4)
3.Heckeoperatorsonformsofhalfintegerweight
4.ThetheoremsofShimura,Waldspurger,Tunnell,andthecol-ruent
numberproblem
Answers,Hints,andReferencesforSelectedExercises
Bibliography
Index