P-Adic integration on ray class groups and non-ordinary P-Adic L-functions

We study the theory of p-adic finite-order 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 GL2 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 GL2 over an imaginary quadratic field with p split and Hecke eigenvalues 0 at the primes above p, confirming a conjecture of B.D. Kim