Time

Location

Speaker

Abstract

L-functions are very interesting, and equally mysterious, complex analytic invariants attached to certain arithmetic objects, geometric objects, and analytic objects. L-functions seem to have a wonderful ability to interpolate from the local to the global. The paradigm of an L-function is the Riemann zeta function and the arithmetic contained in it, such as the prime number theorem. Most of our understanding and expectations of L-functions come from examples.

In these two talks I hope to give a feeling for what L-functions are and some of the things we expect from them by discussing several examples, including the Riemann zeta function, the Dirichlet L-functions, the L-function of an elliptic curve, and perhaps Artin L-functions. I will also discuss the analytic side, so L-functions attached to modular or automorphic forms. If there is time, perhaps I may even be able to give a small introduction to the Langlands program.

Notes