《自守形式与L-函数简明六章(精)》由Ze-Li Dou、Qiao Zhang所著，这本小书的主题是数论中两个重要的课题，即L-函数理论中的MomentConjecture和GoroShimura（志村五郎）的periodconjectures，是笔者根据在中国、美国、土耳其等做的一些报告和讲座补充、改编而成的。这两个猜想的深度和广度都非常可观，入门不易。基于这个原因，本书的编写以提纲挈领、简洁明快为主旨，对中心概念的由来、课题的意义与目标的阐述占据了较大的篇幅，而技术性的枝节则多有删除。为了便于阅读，笔者又将全书分为长度相仿的六个短章，且每章的内容基本独立。读者阅读本书以后，能对这两大猜想有一个概括性的了解。同时，笔者也希望本书能给有志于详细钻研这些课题的读者提供一个引子。

Chapter 1 Modular forms and the Shimura-Taniyama Conjecture

1.1 Elliptic functions

1.2 Modular forms

1.3 Examples

1.4 Hecke operators and eigenforms

1.5 L-functions

1.6 Modular forms of higher level

1.7 Elliptic curves

1.8 Conjectures, and the theorem of Wiles, et al

References

Chapter 2 Periods of automorphic forms

2.1 Automorphic forms

2.2 Periods arising from Dirichlet series

2.3 Periods arising from elliptic curves

2.4 Periods arising from cohomology theory

2.5 Recapitulation

2.6 Hilbert modular forms

2.7 Autornorphic forms with respect to a quaternion algebra

2.8 Adelic automorphic forms

2.9 Hecke operators

2.10 The standard L-function for Hilbert modular forms and the

    V periods

2.11 The inner product and the Q periods

2.12 The Eichler-Shimura Isomorphism and the P periods

References

Chapter 3 Lifting of automorphic forms

3.1 Dirichlet series

3.2 Hecke characters with respect to a real quadratic numbereld

3.3 L-series and the base change lift for characters

3.4 Hilbert modular forms over a real quadratic field and the

   Doi-Naganuma lift

3.5 Applications of base change

3.6 Shimura's period conjectures

3.7 Yoshida's work

References

Chapter 4 Zeros of L-functions

4.1 Trivial zeros

4.2 The Grand Riemann Hypothesis

4.3 Zero-free regions

4.4 Siegel zeros

4.5 Correlations of zeros

4.6 Random matrix theory

References

Chapter 5 Special values of L-functions

5.1 The Birch-Swinnerton-Dyer conjecture

5.2 The Gross-Zagier formula

5.3 The class number problem

5.4 The LindelSf conjecture and subconvexity bounds

5.5 Discrete moment conjecture of L-functions

5.6 Integral moment conjectures of L-functions

References

Chapter 6 Theta lifts and periods with respect to a

       quadratic extension

6.1 Setting

6.2 Automorphic forms with respect to Be

6.3 Theta function

6.4 Transformation formulas

6.5 Theta correspondence

6.6 Reduction of the integral

6.7 Two technical lemmata

6.8 Main theorems on theta correspondence

6.9 Adelic forms on G'A

6.10 Embeddings and inner product

6.11 Theta correspondence of adelic forms

6.12 Hecke Operators on GL2(F)

6.13 The action of Hecke operators on I(z; C; r; h)

6.14 Hecke operators on adelic forms

6.15 Relation between actions of Hecke operators

6.16 Further Reading

References