CLASS HOURS: Tue, Thu 9:30 -- 11:00 RLM 9.166

OFFICE HOURS: Wed 10:00 -- 11:00 or by appointment.

TEXTBOOK: There will be no textbook, but part of the material I plan to cover can be found in various books such as Cassels' Local Fields, Koblitz's p-adic numbers, p-adic analysis and Zeta functions, Gouvêa's p-adic numbers, Borevich-Shafarevich's Number Theory and many others. You can even find on-line, Zahlentheorie, by K. Hensel, the creator of p-adic numbers.

SYLLABUS: This course will cover the basic theory of p-adic fields and their extensions and basic p-adic analysis. We will discuss applications to diophantine equations, such as Skolem's method. Time permitting, we will also cover formal groups and local class field theory.

Here is an elementary discussion of p-adic numbers with a few examples, written by David Madore.

Here are some notes on formal groups by Antonia W. Bluher.

And here are some rough notes on Witt vectors.

The room has changed to the 9th floor classroom, RLM 9.166.

Some other good books on p-adic numbers. Please don't go and check them all out of the library at once!

- p-adic numbers and their functions. Mahler, Kurt. QA 241 M22 1981
- Local fields. Serre, Jean Pierre. QA 247 S4613
- Les Nombres p-adiques, Y. Amice.
- Introduction to p-adic numbers and valuation theory, G. Bachman.

This page has been visited times since May, 11th, 1997.

Behold **Z _{3}**! (I also have a bigger picture
.)