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Elliptic tales : curves, counting, and number theory /

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
Main Authors: Ash, Avner
Corporate Authors: De Gruyter.
Group Author: Gross, Robert
Published: Princeton University Press,
Publisher Address: Princeton, N.J. :
Publication Dates: [2015]
©2015
Literature type: eBook
Language: English
Subjects:
Counting.
Curves, Elliptic.
Elliptic functions.
MATHEMATICS > Algebra > Abstract.
MATHEMATICS > Complex Analysis.
Number theory.
History and Philosophy.
Mathematics.
Mathematik.
Online Access: http://dx.doi.org/10.1515/9781400841714
http://www.degruyter.com/doc/cover/9781400841714.jpg
Summary: 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.
Carrier Form: 1 online resource(280pages) : illustrations
ISBN: 9781400841714
Index Number: QA343
CLC: O174.54
Contents: Frontmatter --
Contents --
Preface --
Acknowledgments --
Prologue --
Chapter 1. Degree of a Curve --
Chapter 2. Algebraic Closures --
Chapter 3. The Projective Plane --
Chapter 4. Multiplicities and Degree --
Chapter 5. B zout s Theorem --
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 --
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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