Elliptic Tales : : Curves, Counting, and Number Theory / / Avner Ash, Robert Gross.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Ash, Avner,; Gross, Robert,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2012]; ©2012
• Year of Publication: 2012
• Edition: Course Book
• Language: English
• Physical Description: 1 online resource (280 p.) :; 52 line illus. 16 tables.
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400841714; 9783110442502
• DOI: 10.1515/9781400841714
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: 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 captivating problem.The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep-and often very mystifying-mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics.