On Teitelbaum type L-invariants of Hilbert modular forms attached to definite quaternions

We generalize Teitelbaum's work on the definition of the L-invariant to Hilbert modular forms that arise from definite quaternion algebras over totally real fields by the Jacquet-Langlands correspondence. Conjecturally this coincides with the Fontaine-Mazur type L-invariant, defined by applying Fontaine's theory to the Galois representation associated to Hilbert modular forms. An exceptional zero conjecture for the p-adic L-function of Hilbert modular forms is also proposed.