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Complex multiplication /
"This is a self-contained account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of ellip...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
Ã2010.
|
| Colección: | New mathematical monographs ;
15. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "This is a self-contained account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. The main results are accompanied by numerical examples, equipping any reader with all the tools and formulas they need. Topics covered include: the construction of class fields over quadratic imaginary number fields by singular values of the modular invariant j and Weber's tau-function; explicit construction of rings of integers in ray class fields and Galois module structure; the construction of cryptographically relevant elliptic curves over finite fields; proof of Berwick's congruences using division values of the Weierstrass p-function; relations between elliptic units and class numbers"--Provided by publisher |
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| Descripción Física: | 1 online resource (xiii, 361 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 351-355) and indexes. |
| ISBN: | 9780511776199 0511776195 9780511773617 0511773617 9780511776892 0511776896 9781107471771 110747177X 1107208912 9781107208919 1139636669 9781139636667 1282651862 9781282651869 9786612651861 6612651865 0511775431 9780511775437 0511772548 9780511772542 0511774672 9780511774676 |