** Instructor: **
Ching-Li Chai

*Office*: DRL 4N36, Ext. 8-8469.

*Office Hours*: W 11:00-12:00.

Email:`chai@sas.upenn.edu`

Exercises

- Exercise 1
- Exercise 2
- Exercise 2A
- Exercise 3
- Exercise 3A
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11

**Lectures**: MW 1:30--3:00 PM, 4C8 DRL

First meeting: Wednesday, September 7, 2005.

**Topics**: This year Math 620 will run in the "elmentary mode". The topics include: local fields, splitting and ramification of primes, finiteness of class numbers, Dirichlet's unit theorem, adels and idels, Dedekind zeta functions and Hecke L-functions, functional equation of L-functions, local class field theory, global class field theory, Artin L-functions, non-vanishing of L-functions, distribution of primes, primes in arithmetic progression, Brauer-Siegel theorem.

**Background knowledge**: basic algebras and analysis at the level of standard first year graduate courses.

**Reference Books**: There will be no texbook for this course. The following books are recommended as references.- Lang, Algebraic Number Theory
- Cassel and Frohlich (eds.), Algebraic Number Theory
- Serre, Local Fields
- Neukirch, Algebraic Number Theory
- Artin and Tate, Class Field Theory
- Davenport and Montgomery, Multiplicative Number Theory
- Washington, Cyclotomic Fields
- Hida, Elementary Theory of L-functions

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