Elliptic Tales : : Curves, Counting, and Number Theory / / Avner Ash, Robert Gross.
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics-the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this...
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Superior document: | Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2012] ©2012 |
Year of Publication: | 2012 |
Edition: | Course Book |
Language: | English |
Online Access: | |
Physical Description: | 1 online resource (280 p.) :; 52 line illus. 16 tables. |
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Table of Contents:
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Prologue
- PART I. DEGREE
- Chapter 1. Degree of a Curve
- Chapter 2. Algebraic Closures
- Chapter 3. The Projective Plane
- Chapter 4. Multiplicities and Degree
- Chapter 5. Bézout's Theorem
- PART II. ELLIPTIC CURVES AND ALGEBRA
- Chapter 6. Transition to Elliptic Curves
- Chapter 7. Abelian Groups
- Chapter 8. Nonsingular Cubic Equations
- Chapter 9. Singular Cubics
- Chapter 10. Elliptic Curves over Q
- PART III. ELLIPTIC CURVES AND ANALYSIS
- Chapter 11. Building Functions
- Chapter 12. Analytic Continuation
- Chapter 13. L-functions
- Chapter 14. Surprising Properties of L-functions
- Chapter 15. The Conjecture of Birch and Swinnerton-Dyer
- Epilogue
- Bibliography
- Index