椭圆曲线和模型式引论 第2版（影印版）

出版时间：2003-6  出版社：世界图书出版公司  作者：N.Koblitz  页数：248  
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内容概要

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.

书籍目录

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

用户评论 (总计4条)

•   薄书适合阅读啊
•   挺有趣的
•   牛人的就是不一般！
•   写得还不错，是两年前看的这本书的，第一章还是很容易看懂的，之后就没有时间看了。