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Elliptic curves over Q
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"Ebook Elliptic curves number theory and cryptography (Second edition)" present Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.
524p
haphuonglan2021
25-04-2021
48
14
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Let E be an elliptic curve over Q, let p be an ordinary prime for E, and let K be an imaginary quadratic field. Write K∞/K for the anticyclotomic Zp-extension of K and set G∞ = Gal(K∞/K). Following a construction of Section 2 of [BD1] which is recalled in Section 1, one attaches to the data (E,K, p) an anticyclotomic p-adic L-function Lp(E,K) which belongs to the Iwasawa algebra Λ := Zp[[G∞]]. This element, whose construction was inspired by a formula proved in [Gr1], is known, thanks to work of Zhang ([Zh, §1.
65p
noel_noel
17-01-2013
45
5
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