Primes of the Form x2 +
ny2:
Fermat, Class Field Theory, and Complex Multiplication
by David A. Cox
Amherst College
with contributions by Roger Lipsett
Original Edition, 1989
Paperback Edition, 1997
Second Edition, 2013
Third Edition with Solutions, 2022
The Third Edition
The third edition of Primes of the Form x2 +
ny2 was published in 2022 by the American Mathematical Society. The main features of the third edition are:
- Solutions to all exercises, written by Roger Lipsett and David Cox, are included.
- Section 15 on Shimura Reciprocity has been rewritten for clarity.
- There is now a unified Reference section.
- All exercises have been checked for clarity and correectness.
- A few new exercises and references have been added.
- All known errata in the second edition have been corrected.
Errata in the Third Edtion
A list of known errata in the third edition is available in pdf
The Second Edition
The second edition of Primes of the Form x2 +
ny2 was published in 2013 by John Wiley & Sons. 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 Ramanujan 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.
Errata in the Second Edition
The list of known errata as of June 19, 2022 in the second edition is
available in pdf .
Errata in the First Edition
Lists of errata 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
errata in the hardcover edition were corrected. The
remaining errata are available in
pdf or postscript .
All of these errata 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 Third Edition
Click here
for the AMS catalog page for the third 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
You can contact me at
dacox@amherst.edu