On the non-vanishing mod ℓ of central L-values with anticyclotomic twists for Hilbert modular forms

In this article, we generalize some works of Masataka Chida and Ming-Lun Hsieh on anticyclotomic p-adic L-functions attached to modular forms to Hilbert case. We construct a class of anticyclotomic p-adic L-functions for ordinary Hilbert modular forms and derive the interpolation formula at all critical specializations. Moreover, we prove results on the vanishing of μ-invariant of these p-adic L-functions and the non-vanishing of central L-values with anticyclotomic twists.