M 390 C p-adic numbers

INSTRUCTOR: Felipe Voloch (RLM 9.122, ph.471-2674)

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.

New! 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.

If you want to do some calculations, I recommend Pari. Note that this page is still under development and requires netmath to be viewed in full glory. The previous link will lead you to a page from which you can download netmath as a standalone program. If you want, it is possible but not recommended, to view netmath under netscape by going here, but you'll need some plug-ins in your browser.

This page has been visited [an error occurred while processing this directive] times since May, 11th, 1997.

Behold Z₃! (I also have a bigger picture .)