|Series||New mathematical monographs -- 15|
|LC Classifications||QA564 .S294 2010|
|The Physical Object|
|LC Control Number||2009051874|
Get this from a library! Complex multiplication. [Reinhard Schertz] -- "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. In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the tangent space at the identity element of A is a direct sum of one-dimensional . This self-contained account of the state of the art in classical complex multiplication provides an exhaustive treatment of the theory of elliptic functions, modular functions and quadratic number fields. The reader will find all the necessary background and tools they will need in this : Cambridge University Press. This would be a vague question, but I still want to ask here. Do you have any recommended book on complex multiplicaton. I know only 2 books: Shimura's book Abelian Varieties with Complex Multiplication and Modular Functions and Lang's book Complex a's book used old-language (published in ), and I feel it would be nice to read this book when I .
ISBN: OCLC Number: Description: viii, pages: illustrations: Contents: 1 Analytic Complex Multiplication.- 1. Positive. CHAPTER THREE COMPLEX MULTIPLICATION § ELLIPTIC FUNCTIONS AND COMPLEX MULTIPLICATION In Chapter Two we solved our problem of when a prime p can be written in the form x2 - Selection from Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication [Book]. Karatsuba's algorithm was the first known algorithm for multiplication that is asymptotically faster than long multiplication, and can thus be viewed as the starting point for the theory of fast multiplications. In , Peter Ungar suggested setting m to i to obtain a similar reduction in the complex multiplication algorithm. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x 2 + ny 2, Second Edition focuses on addressing the question of when a prime p is of the form x 2 + ny 2.
Referring to for the de nition of the multiplication by an idele map, we can state the main theorem of complex multiplication for elliptic curves: Theorem (Main theorem of complex multiplication for elliptic curves) Fix the following objects: Ka quadratic imaginary eld Ean elliptic curve over C such that End Q(E) ˘= Size: KB. Email your librarian or administrator to recommend adding this book to your organisation's collection. 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. H.M., Stark, A complete. This is from Gauss, not Karatsuba. Karatsuba multiplication is for the quad precision product of two double precision integers. In when this was discovered, multiplication in computers was a slow operation consisting of shift and add-- 32 such operations for a 32 bit integer, as in Russian peasant multiplication. The book under review is a comprehensive account of the classical theory of complex multiplication for elliptic curves, with some concessions to the current trends in applications, including a chapter on elliptic curve cryptography.