ON THE QUATERNIONIC p-ADIC L-FUNCTIONS ASSOCIATED TO HILBERT MODULAR EIGENFORMS

Abstract

We construct p-adic L-functions associated to cuspidal Hilbert modular eigenforms of parallel weight two in certain dihedral or anticyclotomic extensions via the Jacquet–Langlands correspondence, generalizing works of Bertolini–Darmon, Vatsal and others. The construction given here is adelic, which allows us to deduce a precise interpolation formula from a Waldspurger-type theorem, as well as a formula for the dihedral μ-invariant. We also make a note of Howard's non-vanishing criterion for these p-adic L-functions, which can be used to reduce the associated Iwasawa main conjecture to a certain non-triviality criterion for families of p-adic L-functions.