Mathematics 254B, Spring 2008 Number theory

Professor: Richard Borcherds

Office hours: Tuesday, Thursday 2:00-3:30 927 Evans Hall

This class meets in 81 Evans Hall, TuTh 3:30-5:00. The first lecture is on Tuesday Jan 22, the last lecture is on Thursday May 8, and there are no lectures on March 25 and March 27 because of the spring recess. This is the course home page (address http://math.berkeley.edu/~reb/254B/). The course control number is 54967.

Catalogue Description: Mathematics 254B

Course Format: Three hours of lecture per week.

Prerequisites: 254A number theory

Description: Valuations, units, and ideals in number fields, ramification theory, quadratic and cyclotomic fields, topics from class field theory, zeta-functions and L-series, distribution of primes, modular forms, quadratic forms, diophantine equations, P-adic analysis, and transcendental numbers. Sequence begins fall.

This course

I plan to cover the functional equation of the zeta function of a number field, and class field theory.

Textbook:

J. Neukirch "Algebraic number theory" (same as for 254A)

Recommended Reading: Cassels, Frohlich, "Algebraic number theory". This is out of print, but photocopies should be available from Copy Central, 2560 Bancroft.

Links related to the course:

Examinations:

None.

Suggested homework:

  1. January 22-24: Chapter VII.1, exercises 1-5.
  2. January 29-31: Chapter VII.2 exercisea 1-4
  3. February 5-7: Chapter VII.3
  4. February 12-14: Chapter II.1 exercises 1-6