Table of Contents

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.

About the Author

DAVID A. COX is Professor of Mathematics at Amherst College.