UC Santa Cruz

We give a new definition of a p-adic L-function for a mixed signature character of a real quadratic field and for a nontrivial ray class character of an imaginary quadratic field. We then state a p-adic Stark conjecture for this p-adic L-function. We prove our conjecture in the case when p is split in the imaginary quadratic field by relating our construction to Katz's p-adic L-function. We also prove our conjecture in the real quadratic setting for one special case and give numerical evidence in one specific example.