This is a self-contained 2010 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.
General
| Imprint: |
Cambridge UniversityPress
|
| Country of origin: |
United Kingdom |
| Series: |
New Mathematical Monographs |
| Release date: |
April 2010 |
| First published: |
June 2010 |
| Authors: |
Reinhard Schertz
|
| Dimensions: |
229 x 152 x 25mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
376 |
| Edition: |
New |
| ISBN-13: |
978-0-521-76668-5 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Number theory >
General
|
| LSN: |
0-521-76668-0 |
| Barcode: |
9780521766685 |
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