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

by David A. Cox
Amherst College

John Wiley & Sons

Original Edition, 1989
Paperback Edition, 1997
Second Edition, 2013

The Second Edition

The second edition of Primes of the Form x² + ny² 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.

Typographical Errors in the Second Edition

The list of known typographical errors in the second edition is available in pdf .

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.

• Typos for the first printing: pdf or postscript .
• Typos for the second printing: pdf or postscript .

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 x² + ny². This page includes a brief description of the book and information on how to order a copy.

Contacting the Author

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