9780691085593-0691085595-Elliptic Curves. (MN-40)

Elliptic Curves. (MN-40)

ISBN-13: 9780691085593
ISBN-10: 0691085595
Edition: 1
Author: Knapp, Anthony W.
Publication date: 1992
Publisher: Princeton University Press
Format: Paperback 448 pages
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Book details

ISBN-13: 9780691085593
ISBN-10: 0691085595
Edition: 1
Author: Knapp, Anthony W.
Publication date: 1992
Publisher: Princeton University Press
Format: Paperback 448 pages

Summary

Acknowledged authors Knapp, Anthony W. wrote Elliptic Curves. (MN-40) comprising 448 pages back in 1992. Textbook and eTextbook are published under ISBN 0691085595 and 9780691085593. Since then Elliptic Curves. (MN-40) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem.


Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways.


Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner.

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