椭圆曲线和模型式引导·第2版（英文版）
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内容提要：
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.
编辑推荐：
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.
本书为英文版。 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 problem CHAPTER 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 value CHAPTER 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 operators CHAPTER 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 problem Answers, Hints, and Referen es for Selected Exercises Bibliography Index 前言：
Preface to the First Edition This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book.
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 exerci..
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