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Key Information
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| Authors: |
Anthony W. Knapp |
| Nonfiction Category: |
Mathematics |
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Book Editions
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Format: Paperback, 427
Publisher: Princeton Univ Pr (October 05, 1992)
Measurements: 9.5"(h) x 6"(w) x 1.25"(d), 1.45 lbs.
ISBN: 9780691085593 |
| More Information |
| Details: |
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 w |
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