A p-adic Stark conjecture in the context of quadratic fields

Abstract: In the 1980's Stark made precise conjectures about the leading term of the Taylor expansion at s=0 for Artin L-functions, refining Dirichlet's class number formula. Around the same time Barsky, Cassou-Nogues, and Deligne and Ribet for totally real fields, along with Katz for CM fields defined p-adic L-functions of ray class characters. Since then Stark-type conjectures for these p-adic L-functions have been formulated, and progress has been made in some cases. The goal of this talk is to discuss a new definition of a p-adic L-function and Stark conjecture in the context of a mixed signature character of a real quadratic field or any ray class character of an imaginary quadratic field. After stating the definition and conjecture, theoretical and numerical evidence will be discussed.