Math 620/621, Algebraic Number Theory, 2005/2006

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

General Information

• 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