"Eisenstein series and analytic continuation of Dirichlet series"

By examining the Fourier coefficients of Eisenstein series (on a semisimple Lie group) twisted by characters, we observe Dirichlet series with interesting arithmetic quantities. We give a method for obtaining these continuations using functional equations (the "method of multiple Dirichlet series") and discuss recent arithmetic applications following from complex contour integration methods on the resulting series. We'll conclude with the broad brushstrokes of a program to determine what is possible via these methods. The results presented are joint work with Dan Bump, Sol Friedberg, and Jeff Hoffstein.