  We study the theory of finite-order p-adic functions and distributions on ray
class groups of number fields, and apply this to the construction of (possibly
unbounded) p-adic L-functions for automorphic forms on GL(2) which may be
non-ordinary at the primes above p. As a consequence, we obtain a "plus-minus"
decomposition of the p-adic L-functions of automorphic forms for GL(2) over an
imaginary quadratic field with p split and Hecke eigenvalues 0 at the primes
above p, confirming a conjecture of B.D. Kim.
