For each Hilbert modular form of non-critical slope we construct a p-adic distribution on the Galois group of the maximal abelian extension unramified outside p and 8 of the totally real field. We prove that the distribution is admissible and interpolates the critical values of the complex L-function of the form. This construction is based on the study of the overconvergent cohomology of Hilbert modular varieties and certain cycles on these varieties
Barrera, D. Overconvergent cohomology of Hilbert modular varieties and p-adic L-functions. "Annales de l'Institut Fourier", 2018.