模形式基础教程

图书标准信息

• 作者 戴梦德、谢尔曼 编
• 出版社 世界图书出版公司
• 出版时间 2007-05
• 版次 1
• ISBN 9787506283007
• 定价 49.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 436页
• 正文语种 英语

【内容简介】

《模形式基础教程》是《数学研究生丛书》第228卷，内容主要包括：椭圆曲线、复环面和代数曲，模曲线、黎曼曲面和代数曲线，Hecke算子和Athkin—Lehner理论，Hecke特征形式及它们的算术性质，模曲线的雅可比行列式和Hecke特征形式的阿贝尔簇，椭圆曲线、模曲线模P及Eichler—Shimura关系，椭圆曲线和Hecke特征形式的Galois表示。

【目录】

Preface
ModularForms，EllipticCurves，andModularCurves...
1.1Firstdefinitionsandexamples
1.2Congruencesubgroups
1.3Complextori
1.4Complextoriasellipticcurves
1.5Modularcurvesandmodulispaces

2ModularCurvesasRiemannSurfaces
2.1Topology
2.2Charts
2.3Ellipticpoints
2.4Cusps
2.5ModularcurvesandModularity

3DimensionFormulas
3.1Thegenus
3.2Automorphicforms
3.3Meromorphicdifferentials
3.4DivisorsandtheRiemann-RochTheorem
3.5Dimensionformulasforevenk
3.6Dimensionformulasforoddk
3.7Moreonellipticpoints
3.8Moreoncusps
3.9Moredimensionformulas

4EisensteinSeries
4.1EisensteinseriesforSL2（Z）
4.2EisensteinseriesforF（N）whenk≥3
4.3Dirichletcharacters，Gausssums，andeigenspaces
4.4Gamma，zeta，andL-functions
4.5Eisensteinseriesfortheeigenspaceswhenk≥3
4.6Eisensteinseriesofweight2
4.7BernoullinumbersandtheHurwitzzetafunction
4.8Eisensteinseriesofweight1
4.9TheFouriertransformandtheMellintransform
4.10NonholomorphicEisensteinseries
4.11Modularformsviathetafunctions

5HeckeOperators
5.1Thedoublecosetoperator
5.2TheandTpoperators
5.3The（n>andTnoperators
5.4ThePeterssoninnerproduct
5.5AdjointsoftheHeckeOperators
5.6OldformsandNewforms
5.7TheMainLemma
5.8Eigenforms
5.9TheconnectionwithL-functions
5.10Functionalequations.
5.11Eisensteinseriesagain

6JacobiansandAbelianVarieties
6.1Integration，homology，theJacobian，andModularity
6.2MapsbetweenJacobians
6.3ModularJacobiansandHeckeoperators
6.4Algebraicnumbersandalgebraicintegers
6.5Algebraiceigenvalues
6.6Eigenforms，Abelianvarieties，andModularity

7ModularCurvesasAlgebraicCurves
7.1Ellipticcurvesasalgebraiccurves
7.2Algebraiccurvesandtheirfunctionfields
7.3Divisorsoncurves
7.4TheWeilpairingalgebraically
7.5FunctionfieldsoverC
7.6FunctionfieldsoverQ
7.7ModularcurvesasalgebraiccurvesandModularity
7.8Isogeniesalgebraically
7.9Heckeoperatorsalgebraically

8TheEichler-ShimuraRelationandL-functions
8.1Ellipticcurvesinarbitrarycharacteristic
8.2Algebraiccurvesinarbitrarycharacteristic
8.3EllipticcurvesoverQandtheirreductions
……
9GaloisRepresentations
HintsandAnswerstotheExercises
ListofSymbols
Index
References