Elliptic Tales : : Curves, Counting, and Number Theory /

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

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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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Bibliographic Details
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
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

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