** Analytic Continuation of L-functions through Distributions**

** Stephen Miller
**

The analytic continuation of L-functions is a central goal in number
theory, which usually comes through two approaches. The first,
originally due to Riemann in his famous paper on the zeta function,
expresses the L-function as an integral of an automorphic form.
Properties of the form then translate to the L-function. Another
approach, due to Langlands-Shahidi, finds L-functions in the Fourier
expansions of exotic Eisenstein series, and obtains the analytic
continuation from spectral theory. These methods have yielded
outstanding successes, but still leave fundamental unsolved gaps between
them. I will discuss a third method, developed in joint work with
Wilfried Schmid, which uses pairings of automorphic distributions, to
obtain the full analytic continuation and functional equation of some
new examples of Langlands L-functions.