Applications of Eisenstein Series to Number Theory and Combinatorics

We'll discuss recent joint work with Dan Bump, Sol Friedberg, and Jeff Hoffstein on computing the Fourier (Whittaker) coefficients of certain Eisenstein series and a (still partly conjectural) combinatorial recipe for producing them. The Fourier coefficients are Dirichlet series in several complex variables whose numerators contain interesting arithmetic objects such as Dirichlet L-functions, coefficients of modular forms, and theta functions, which can then be studied using standard complex integration techniques.