David A. Cox 
Primes of the Form x2+ny2 [PDF ebook] 
Fermat, Class Field Theory, and Complex Multiplication

An exciting approach to the history and mathematics of number
theory
‘. . . the author’s style is totally lucid and very
easy to read . . .the result is indeed a wonderful story.’
–Mathematical Reviews
Written in a unique and accessible style for readers of varied
mathematical backgrounds, the Second Edition of Primes of
the Form p = x2+ ny2
details the history behind how Pierre de Fermat’s work
ultimately gave birth to quadratic reciprocity and the genus theory
of quadratic forms. The book also illustrates how results of Euler
and Gauss can be fully understood only in the context of class
field theory, and in addition, explores a selection of the
magnificent formulas of complex multiplication.
Primes of the Form p = x2 +
ny2, Second Edition focuses on
addressing the question of when a prime p is of the form
x2 + ny2,
which serves as the basis for further discussion of various
mathematical topics. This updated edition has several new notable
features, including:
* A well-motivated introduction to the classical
formulation of class field theory
* Illustrations of explicit numerical examples to
demonstrate the power of basic theorems in various situations
* An elementary treatment of quadratic forms and genus
theory
* Simultaneous treatment of elementary and advanced
aspects of number theory
* New coverage of the Shimura reciprocity law and a
selection of recent work in an updated bibliography
Primes of the Form p = x2 +
ny2, Second Edition is both a useful
reference for number theory theorists and an excellent text for
undergraduate and graduate-level courses in number and Galois
theory.

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About the author