##
Primes of the Form x^{2} +
ny^{2}:

Fermat, Class Field Theory, and Complex Multiplication

##
Original Edition, 1989

Paperback Edition, 1997

Second Edition, 2013

## The Second Edition

The second edition of *Primes of the Form x*^{2} +
ny^{2} was published in 2013. The main
features of the second edition are:

- There is a new Section 15 on Shimura reciprocity, based on the work of
Peter Stevenhagen and Alice Gee.
- The new
*Additional References* section contains
references not cited in the first edition. Some of these new
references are mentioned in the text; the others are intended for
further reading.
- The new Exercise 12.31 at the end Section 12
shows how Ramanujam could
have done one of Weber's singular moduli computations.
- All of the known errata in the first edition have been corrected.

The other changes in the text are minor, mostly to enhance clarity,
improve formatting, and simplify some of the proofs.

## Typographical Errors in the Second Edition

The list of know typographical errors in the second edition is
available in pdf or postscript .

## Typographical Errors in the First Edition

Lists of typographical errors are available for the two printings
of the **hardback first edition**. To find out which printing you
have, check the bottom line on the copyright page; the last digit
displayed is the printing number.

These lists contain errata discovered as of January 28, 2009. Any
typos discovered after this date appear in the errata list for the
softcover edition.
For the **softcover first edition**, many (but not all) of the
typographical errors in the hardcover edition were corrected. The
remaining errors are available in
pdf or postscript .

All of these typos were corrected in the second
edition of the book, which appeared in 2013.

## Additional Exercises

For a nice set of exercises that supplement Chapter One of the
book, click here.
I am grateful to Jeffrey Stopple for preparing these exercises.

## Ordering Information for the Second Edition

** Hardcover Version.** Click here
for the Wiley catalog page for the second edition of **Primes of the Form x**^{2} +
ny^{2}. This page
includes a brief description of the
book and information on how to order a copy.

## Contacting the Author

You can contact me at

dac@math.amherst.edu