Math 620 - Algebraic Number Theory
MWF 1:00pm - 1:50pm, Room: Math 0405
Lecturer: Larry Washington (For email address, hold cursor here and look at the bottom of the page)
Office: Math 4415, Phone: 301-405-5116
Office Hours:
I'm in my office most of the time.
Syllabus:
When working in number theory, one is led quickly to the
study of rings of algebraic integers in finite extensions
of the rationals, for example, the Gaussian integers.
The study of these rings, and
applications, will occupy the first half of the course.
Analytic techniques such as zeta functions will then be introduced.
Each of the last four topics listed below will be treated
briefly, if time permits.
Topics from ring theory, especially Dedekind domains, prime ideals, unique factorization, and ramification.
Finiteness of the class number and the Dirichlet Unit Theorem
Cyclotomic reciprocity and quadratic reciprocity
Zeta functions, $L$-series, and Dirichlet's theorem
on primes in arithmetic progressions
$p$-adic numbers
Equations over finite fields
Elliptic curves and other diophantine equations
Modular forms with applications to sums of squares.
Prerequisite: Math 601, in particular some ring theory
and Galois theory.
Text: There is a free, online text that is close to what I'll do in my lectures:
Algebraic Number Theory notes by James Milne
Another good online source is
Matt Baker's notes
Homework:
Homework 1
Homework 2
Homework 3