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  • 椭圆函数(第2版)[平装]
  • 共2个商家     35.60元~45.00
  • 作者:S.Lang(作者)
  • 出版社:世界图书出版公司;第2版(2003年11月1日)
  • 出版时间:
  • 版次 :
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  • 包装:
  • ISBN:9787506265508

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    目录

    PART ONEccGENERAL THEORY
     Chapter1 Ellipti Functions
      1 ThecLiouville Theorems
      2 The Weierstrass Function
      3 The AdditioncTheorem
      4 Isomorphism Classescof Elliptic Curves
      5 Endomorphisms and Automorphisms  
     Chapter2 Homomorphisms
      1 Points of Finite Order
      2 Isogenies
      3 The Involution
     Chapter 3 hecModular Function
      1 The Modular Group
      2 Automorphic Functions of Degree 2k
      3 The Modular Functionj
     Chapter 4 Fourier Expansions
      1 Expansion for Gk,cg2,cg3,c△candcj
      2 Expansion for the Weierstrass Function
      3 Bernoulli Numbers
     Chapter 5 The Modular Equation
      1 Integral Matrices with Positive Determinant
      2 The Modular Equation
      3 Relations with Isogenies
     Chapter 6 Higher Levels
      1 Congruence Subgroups
      2 The Field of Modular Functions OvercC
      3 The Field of Modular Functions OvercQ
      4 Subfields of the Modular Function Field
     Chapter 7 Automorphisms of the Modular Function Field
      1 Rational Adeles of GL
      2 Operation of the Rational Adelescon the Modular Function Field
      3 The Shimura Exact Sequence
      PARTcTWOccCOMPLEXcMULTIPLICATION ELLIPTICcCURVEScWITHcSINGULARcINVARIANTS
     Chapter 8 Results from Algebraic Number Theory
      1 Latticescin Quadratic Fields
      2 Completions
      3 The Decomposition Group and Frobenius Automorphism
      4 Summary of Class Field Theory
    Chapter 9 Reduction of Elliptic Curves
      1 Non-degenerate Reduction, General Case
      2 Redu tion of Homomorphisms
      3 Coverings of LevelcN
      4 Reduction of Differential Forms
      Chapter 10 Complex Multiplication
      1 Generation of Class Fields, Deuring's Approach
      2 Idelic Formulation for Arbitrary Lattices
      3 Generation of Class Fields by Singular Values of Modular Functions
      4 The Frobenius Endomorphism
      Appendix A Relation of Kronecker
    Chapter 11 Shimura's Reciprocity Law
      I Relation Between Generic and Special Extensions
      2 Application to Quotientscof Modular Forms
    Chapter 12 The Fun tion △(at)/△(t)
      1 Behavior Under the Artin Automorphism
      2 Prime Factorization of its Values
      3 Analyti Proof for the Congruence Relationcofj
     Chapterc13 The l-adic and p-adic Representations of Deuring
    1 Thecl-adic Spaces
    2 Representations in Characteristi p
    3 Representations and Isogenies
    4 ReductioncofcthecRingcofcEndomorphisms
    5 The Deuring Lifting Theorem
    Chapter 14 Ihara's Theory
    1. Deuring Representatives
    2 The Generic Situation
    3 Special Situations
    PART THREE ELLIPTIC CURVEScWITH NON-INTEGRAL INVARIANT
    Chapter 15 The Tate Parametrization
    1 Elliptic Curves with Non-integral Invariants
    2 Ellipti Curves Over a Complete Local Ring
    Chapter 16 The Isogeny Theorems
    1 The Galois p-adic Representations
    2 Results of Kummer Theory
    3 The Local Isogeny Theorems
    4 Supersingular Redu tion
    5 The Global Isogeny Theorems
    Chapter 17 Division Points Over Number Fields
    1 AcTheorem of Shafarevic
    2 The Irreducibility Theorem
    3 The Horizontal Galois Group
    4 The Vertical Galois Group
    5 End of the Proof
    PARTcFOURccTHETAcFUNCTIONScANDcKRONECKERcLIMIT FORMULA
    Chapter 18 Product Expansions
    1 The Sigma and Zeta Function
    Appendix The Skew Symmetric Pairing
    2 A Normalization and the q-product for the a-function
    3 q-expansions Again
    4 The q-product forcA
    5 The Eta Function of Dedekind
    6 Modular Functions of Levelc2
    Chapter 19 The Siegel Functions and Klein Forms
    1 The Klein Forms
    2 The Siegel Functions
    3 Special Values of the Siegel Functions
    Chapter 20 The Kronecker Limit Formulas
    1 The Poisson Summation Formula
    2 Examples
    3 The FunctioncKs(x)
    4 The Kronecker First Limit Formula
    5 The Kronecker Second LimitcFormula
    Chapter 21 The First Limit Formula and L-series
    1 Relation with L-series
    2 The Frobenius Determinant
    3 Application to thecL-series
    Chapter 22 The Second Limit Formula and L-series
    1 Gauss Sums
    2 An Expression for the L-series
    APPENDICES ELLIPTIC CURVES IN CHARACTERISTIC p
    Appendixc1 Algebraic Formulas in Arbitrary Chara teristic BYcJ.cTATE
    1 Generalized Weierstrass Form
    2 Canonical Forms
    3 Expansion Near O; The Formal Group
    Appendix 2 The Tracecof Frobenius and the Differential of FirstcKind
    1 The Trace of Frobenius
    2 Duality
    3 The Tate Trace
    4 The Cartier Operator
    5 The Hasse Invariant
    Bibliography
    Index