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## Graduate Texts in Mathematics: Advanced Topics in the Arithmetic of Elliptic Curves (Softcover)This book is a followup to the first volume ## $26.59 |

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Please contact us if you've got questions about this product.## Condition

**VERY GOOD:** This book is in very good condition, showing only slight signs of use and wear. It was printed on acid-free paper.

## Description

From the back cover: “This book continues the treatment of the arithmetic theory of elliptic curves begun in the first volume. The book begins with the theory of elliptic and modular functions for the full modular groups Γ(1), including a discussion of Hecke operators and the *L*-series associated to cusp forms. This is followed by a detailed study of elliptic curves with complex multiplication, their associated Grössencharacters and *L*-series, and applications to the construction of abelian extensions of quadratic imaginary fields. Next come a s treatment of elliptic curves over function fields and elliptic surfaces, including specialization theorems for heights and sections. This material serves as a prelude to the theory of minimal models and Néron models of elliptic curves, with a discussion of special fibers, conductors, and Ogg’s formula. Next comes a brief description of *q*-models for elliptic curves over **C** and **R**, followed by Tate’s theory of *q*-models for elliptic curves with non-integral *j*-variant over *p*-adic fields. The book concludes with the construction of canonical local height functions on elliptic curves, including explicit formulas for both archimedean and non-archimedean fields.”

**BRIEF CONTENTS**

- Preface
- Computer Packages
- Acknowledgments
- I. Elliptic and Modular Functions
- II. Complex Multiplication
- III. Elliptic Surfaces
- IV. The Néron Model
- V. Elliptic Curves over Complete Fields
- VI. Local Height Functions
- Appendix A. Some Useful Tables
- Notes on Exercises
- References
- List of Notation
- Index

## Details

- SKU:
- 2143
- Subject:
- Mathematics
- Author:
- Silverman, Joseph H.
- Publisher:
- Springer-Verlag
- Publish Date:
- 1994 (First Printing)
- Format:
- Softcover
- Weight (pounds):
- 1.66
- Dimensions (W”xL”xH”):
- 6.1″x9.2″x1″
- ISBN-13:
- 9780387943282
- ISBN-10:
- 0387943285
- Grade Level:
- Graduate
- Series:
- Springer Graduate Texts in Mathematics

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