Instructor          John E. M^cCarthy
Class                  TuTh 2.30-4.00
Office                 105 Cupples I
Office Hours      M 2:00-3:00, Tu 1:00-2:00, F: 2:00-3:00.
Phone                 935-6753
Notes by David Opela

Prerequisites

Complex Analysis 421-422 and Real Analysis 451-452.

Content

This is a course about Dirichlet Series. I will assume that you know basic functional analysis (as covered, for example, in Folland's "Real Analysis" book) and the complex analysis of 421-422. Familiarity with Hardy spaces would be an asset, but is not essential.

I shall start out defining Dirichlet series -- functions of the form $f(s) = \sum a_n n^{-s}$. We shall look at some convergence issues, and then we shall move on to looking at Banach spaces of Dirichlet series. A central theme in the course will be how Dirichlet series, even though they are a function of only one variable, behave in many ways like a power series in infinitely many variables.

Basis for Grading

Grading will be trivial provided you participate in class.
 

Bibliography

H. Helson                           Dirichlet Series
E.C. Titchmarsh         The theory of the Riemann zeta-function
P. Duren                      Theory of H^p-spaces
W. Rudin                      Real and Complex Analysis