橢圓曲線和模型式引論 第2版（影印版）

內(nèi)容概要

My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book.

書籍目錄

Preface to the First Edition Preface to the Second Edition CHAPTER I From Congruent Numbers to Elliptic Curves   1. Congruent numbers   2. A certain cubic equation   3. Elliptic curves   4. Doubly periodic functions   5. The field of elliptic functions   6. Elliptic curves in Weierstrass form 　7. The additionclaw　8. Points of finite order　9. Points over finite fields, and the congruent number problemCHAPTER II　The Hasse-Weil L-Function of an Elliptic Curve　I. The congruence zeta-function　2. The zeta-function of E　3. Varying the primep　4. The prototype: the Riemann zeta-function　5. The Hasse-Weil L-function and its functional equation  6. The critical valueCHAPTER III Modular forms　1. SL2(Z) and its congruence subgroups　2. Modular forms for SL2(Z)　3. Modular forms for congruence subgroups　4. Transformation formula for the theta-function　5. The modular interpretation, and Hecke operatorsCHAPTER IV　Modular Forms of Half Integer Weight　1. Definitio　ns and examples　2. Eisenstein series of half integer weight for (4)　3. Hecke operators on forms of half integer weight　4. The theorems of Shimura, Waldspurger, Tunnell, and the congruent number problemAnswers, Hints, and Referen es for Selected ExercisesBibliographyIndex

圖書封面

圖書標(biāo)簽Tags

無

評論、評分、閱讀與下載

---

    橢圓曲線和模型式引論 第2版（影印版） PDF格式下載

---