*p*-adic Numbers: an Introduction

## by Fernando Q. Gouvêa

My introduction
to the p-adic numbers was last reprinted in 2003 by Springer-Verlag. (You
can tell whether you have the new printing because this one has my photo on
the back cover.) We took advantage of this third printing (of the second
edition) to correct a few typos. In so doing, as is inevitable, we
introduced other typos. See below for errata.
This book is aimed at advanced undergraduates and graduate students
interested in beginning to learn about the p-adic numbers. It is written in
a way that I hope makes it usable for independent study as well as for a
class. It covers only the basics of the theory. The idea is to set you up
for the deeper treatments and applications you will find in graduate texts
and research monographs. An annotated list of some of what is available
appears in an appendix.

*p-adic Numbers* is part of the *Universitext* series from Springer.
The ISBN is 3-540-62911-4. You can buy this book through
Amazon.com.
(The page at Amazon.com has a couple of really nice reader reviews.)
You can also
order
it directly from Springer.

I'll try to collect here any typos or mistakes that are brought to my
attention. If you think you've found something,
send me an email!
So far, all I have is one... but I'm sure there are more!

- p. 218, displayed equation before problem 324: the last index should
be
*m*, not *i*. Two lines later, α_{i} <
-*m* should read α_{i} ≤ -*m*.

Fernando Q. Gouvêa ---- fqgouvea@colby.edu
Last modified: Sun Jun 20 11:30:06 Eastern Standard Time 2004