Primes of the Form x² + ny²
Fermat, Class Field Theory, and Complex Multiplication
1st Edition
Published on 8. May 1997
Book
Paperback/Softback
XVI, 352 pages
978-0-471-19079-0 (ISBN)
Description
Provides a general solution to the question of which primes p can be expressed in the form x² + ny². Covered first are the special cases considered by Fermat, which involve only quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the mignificent formulas of complex multiplication.
More details
Series
Edition
1., Auflage
Language
English
Place of publication
New York
United States
Publishing group
John Wiley and Sons Ltd
Target group
College/higher education
Edition type
New edition
Dimensions
Height: 23.6 cm
Width: 15.6 cm
Thickness: 18 mm
Weight
425 gr
ISBN-13
978-0-471-19079-0 (9780471190790)
Schweitzer Classification
Other editions
New editions
Book
05/2013
2nd Edition
Wiley
€61.50
Available immediately
Person
DAVID A. COX is Professor of Mathematics at Amherst College.
Content
FROM FERMAT TO GAUSS.
Fermat, Euler and Quadratic Reciprocity.
Lagrange, Legendre and Quadratic Forms.
Gauss, Composition and Genera.
Cubic and Biquadratic Reciprocity.
CLASS FIELD THEORY.
The Hilbert Class Field and p = x¯2 + ny¯2.
The Hilbert Class Field and Genus Theory.
Orders in Imaginary Quadratic Fields.
Class Fields Theory and the Cebotarev Density Theorem.
Ring Class Field and p = x¯2 + ny¯2.
COMPLEX MULTIPLICATION.
Elliptic Functions and Complex Multiplication.
Modular Functions and Ring Class Fields.
Modular Functions and Singular j-Invariants.
The Class Equation.
Ellpitic Curves.
References.
Index.
Fermat, Euler and Quadratic Reciprocity.
Lagrange, Legendre and Quadratic Forms.
Gauss, Composition and Genera.
Cubic and Biquadratic Reciprocity.
CLASS FIELD THEORY.
The Hilbert Class Field and p = x¯2 + ny¯2.
The Hilbert Class Field and Genus Theory.
Orders in Imaginary Quadratic Fields.
Class Fields Theory and the Cebotarev Density Theorem.
Ring Class Field and p = x¯2 + ny¯2.
COMPLEX MULTIPLICATION.
Elliptic Functions and Complex Multiplication.
Modular Functions and Ring Class Fields.
Modular Functions and Singular j-Invariants.
The Class Equation.
Ellpitic Curves.
References.
Index.