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We construct p-adic L-functions associated to cuspidal Hilbert modulareigenforms of parallel weight two in certain dihedral or anticyclotomicextensions via the Jacquet-Langlands correspondence, generalizing works ofBertolini-Darmon, Vatsal and others. The construction given here is adelic,which allows us to deduce a precise interpolation formula from a Waldspurgertype formula, as well as a formula for the dihedral mu-invariant. We also makea note of Howard's nonvanishing criterion for these p-adic L-functions, whichcan be used to reduce the associated Iwasawa main conjecture to a certainnontriviality criterion for families of p-adic L-functions.

On the quaternionic p-adic L-functions associated to Hilbert modular eigenforms