Complex Multiplication

Nonfiction, Science & Nature, Mathematics, Number Theory
Cover of the book Complex Multiplication by Reinhard Schertz, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Reinhard Schertz ISBN: 9781139636667
Publisher: Cambridge University Press Publication: April 29, 2010
Imprint: Cambridge University Press Language: English
Author: Reinhard Schertz
ISBN: 9781139636667
Publisher: Cambridge University Press
Publication: April 29, 2010
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book Representation Theory of the Symmetric Groups by Reinhard Schertz
Cover of the book Alternative Dispute Resolution of Shareholder Disputes in Hong Kong by Reinhard Schertz
Cover of the book Regression Analysis of Count Data by Reinhard Schertz
Cover of the book Political Competition, Partisanship, and Policy Making in Latin American Public Utilities by Reinhard Schertz
Cover of the book Mantle Convection for Geologists by Reinhard Schertz
Cover of the book Diagnostic Imaging of Child Abuse by Reinhard Schertz
Cover of the book Exploring Bach's B-minor Mass by Reinhard Schertz
Cover of the book Foreigners on America's Death Rows by Reinhard Schertz
Cover of the book The Cambridge Companion to the Literature of New York by Reinhard Schertz
Cover of the book Shaping Modern Shanghai by Reinhard Schertz
Cover of the book A History of Modern Tunisia by Reinhard Schertz
Cover of the book Intelligence Power in Peace and War by Reinhard Schertz
Cover of the book Reformation Europe by Reinhard Schertz
Cover of the book China–Japan Relations after World War Two by Reinhard Schertz
Cover of the book Microfinance, Rights and Global Justice by Reinhard Schertz
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy