Number Theory Seminar

The study of p-adic properties of values of L-functions dates back (at least) to Kummer's study of congruences between values of the Riemann zeta function at negative odd integers. The study of p-adic L-functions really took off, though, a century later with Serre's discovery of p-adic modular forms. With a viewpoint that encompasses several settings, including modular forms (GL_2) and automorphic forms on unitary groups, I will discuss a recipe for constructing p-adic L-functions that relies strongly on the behavior of p-adic automorphic forms. Recent developments will be put in the context of more familiar constructions of Serre, Katz, and Hida.