Primes of the Form x2+ny2

This book explains how Fermat's work gave birth to the quadratic reciprocity and the genus of quadratic forms. It goes on to show how the results of Euler and Gauss can be fully understood in the context of classical field theory and explores some of the magnificent formulas of complex multiplication.

---

Provides a general solution to the question of which primes p can be expressed in the form x + ny . 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.