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Primes of the Form x² + ny²: Fermat, Class Field Theory, and Complex Multiplication

David A. Cox
Publisher: 
John Wiley
Publication Date: 
1997
Number of Pages: 
351
Format: 
Paperback
Price: 
105.00
ISBN: 
0471190799
Category: 
Textbook
BLL Rating: 

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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 = x2 + ny2.

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 = x2 + ny2.

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.

Dummy View - NOT TO BE DELETED