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Introduction to Elliptic Curves and Modular Forms

✍ Scribed by Neal Koblitz (auth.)

Publisher: Springer US
Year: 1984
Tongue: English
Leaves: 258
Series: Graduate Texts in Mathematics 97
Edition: 1st
Category: Library

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✦ Synopsis

The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.

✦ Table of Contents

Front Matter....Pages i-viii
From Congruent Numbers to Elliptic Curves....Pages 1-50
The Hasse—Weil L -Function of an Elliptic Curve....Pages 51-97
Modular Forms....Pages 98-175
Modular Forms of Half Integer Weight....Pages 176-222
Back Matter....Pages 223-250

✦ Subjects

Algebraic Geometry

📜 SIMILAR VOLUMES

Introduction to Elliptic Curves and Modu

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✍ Neal Koblitz (auth.) 📂 Library 📅 1993 🏛 Springer-Verlag New York 🌐 English

<p>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