Math 620/621, Algebraic Number Theory, 2005/2006
Office: DRL 4N36, Ext. 8-8469.
Office Hours: W 11:00-12:00.
- Lectures: MW 1:30--3:00 PM, 4C8 DRL
First meeting: Wednesday, September 7, 2005.
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,
- 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
Back to Ching-Li Chai's Home