Elliptic Curves. (MN-40) pdf epub mobi txt 電子書 下載 2024


Elliptic Curves. (MN-40)

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Anthony W. Knapp
Princeton University Press
1992-10-05
264
USD 85.00
Paperback
9780691085593

圖書標籤: 數學  幾何  代數幾何7  代數幾何  代數  Mathematics  Geometry  Algebraic_Geometry   


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发表于2024-12-24

Elliptic Curves. (MN-40) epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

Elliptic Curves. (MN-40) epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

Elliptic Curves. (MN-40) pdf epub mobi txt 電子書 下載 2024



圖書描述

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 modular 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 coincidence 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.

Elliptic Curves. (MN-40) 下載 mobi epub pdf txt 電子書

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Elliptic Curves. (MN-40) pdf epub mobi txt 電子書 下載
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