Abstract:

In the early 1970s, Harold Stark formulated a conjecture about the first non-vanishing Taylor coefficient at zero of Artin L-functions. About 10 years later, he refined his conjecture for abelian L-functions having order of vanishing one at zero, under certain hypotheses. In 1996, Karl Rubin extended this last refinement of Stark to the higher order of vanishing setting. In this expository talk for a general audience, we will give a survey of this area of research and present a more general conjecture, which we formulated in the past few years. At the end, we will present evidence for our conjecture and indicate one possible direction for further research.

(Reception to precede at 3:30 p.m.)