Lectures
MWF 1:00pm-1:50pm (MTH 0302)
Instructor
Professor Niranjan Ramachandran (atma at math dot umd dot edu)
Office: Math Building 4115 (405-5080)
Office hours: To be announced
Class web page
http://www.math.umd.edu/~atma/math608s.html
Texts
Primes of the form x2+ny2 by David Cox.
Advanced Topics in the
Arithmetic of Elliptic Curves by
J. Silverman.
Rational Points on Elliptic Curves by J. Silverman and J. Tate.
Plan of Course
This is, in a sense, a continuation of Math 620 (Algebraic Number Theory) in which the basic concepts
of number theory (Number fields, finiteness of the class group, Dirichlet unit theorem, local fields, valuations,
reciprocity laws, ramification of primes) were introduced. In this course, the plan is to provide a basic
introduction to class field theory (the study of abelian extensions of number fields) with special emphasis
on abelian extensions of the field Q of rational numbers and of imaginary quadratic fields. These are related
to modular forms, elliptic curves, torsion points and Galois representations. Many topics in mathematics are
brought together in this subject (analysis, geometry and algebra). Class field theory constitutes the 20th century
generalization of the classical quadratic reciprocity law.
We shall also discuss the thesis (Princeton, 1950) of J. Tate, which has played a decisive role in the theory of zeta functions.
The first meeting of the course will be on 9 February 2004. The missed classes will be made up during the semester.
Last modified: 25 January 2004