Math 3094 - Fall 2016
p-adic Numbers

Instructor Keith Conrad
Email kconrad at math dot uconn dot edu.
Office hours 11:00-12:00 M, 2:30-3:30 W, or by appointment in MONT  234.
Course info
Lecture M 3:35-4:50 and F 2:35-3:50 in MONT 111.
 
Texts p-adic Analysis Compared with Real by Svetlana Katok.

Other texts on p-adic analysis are by Gouvea (2013), Koblitz (1996), and Robert (2000), but are not required.

Course Handouts

Background notes on modular arithmetic and metric spaces.

Infinite series (see esp. Theorems 3.6, 4.13 (and Corollary 4.14), and 5.2).

The p-adic expansion of rational numbers. (Updated on Oct. 3)

Hensel's lemma.

Ostrowski's theorem.

Field automorphisms of R and Qp.

Visualizing p-adic integers.

Infinite series in p-adic fields.

Application: Denominators of binomial coefficients at rational numbers.

Application: Units modulo prime powers.

Application of Strassmann's Theorem.

Mahler expansions (guest lecture slides).

Mahler expansions (notes).

The space c0(K).

Application: the size of a finite matrix group over Q.

The local-global principle.

Recent Announcements

8/29: First lecture.

11/14: Typographical error in problem 2a on Set 5. In the upper bound, R should be 1/R. A corrected version of the problem set has been posted.

Brief course description: This course is an introduction to p-adic numbers and p-adic analysis.

Prerequisites: Math 3230 or 3240, or 2142 or 3150, or permission of instructor.

Course grade:  This will be based on homeworks and a take-home final.

Homework: Homework assignments will be posted on the bottom of this web page.



Due Week of Homework Assignment
1. Aug. 29
2. Sept. 5

3. Sept. 12 Set 1.
4. Sept. 19

5. Sept. 26 Set 2.
6. Oct. 3

7. Oct. 10
Set 3.
8. Oct. 17
9. Oct. 24
Set 4.
10. Oct. 31

11. Nov. 7
12. Nov. 14
Set 5.
13. Nov. 21
None (it's Thanksgiving).
14. Nov. 28
15. Dec. 5

16. Dec. 12
Problem Set in Lieu of Final. Do NOT discuss the problems with anyone except the instructor.