On Teitelbaum type \(\mathcal{L}\)-invariants of Hilbert modular forms attached to definite quaternions. (English) Zbl 1380.11048
Summary: We generalize Teitelbaum’s work on the definition of the \(\mathcal{L}\)-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 \(\mathcal{L}\)-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.
MSC:
| 11F41 | Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces |
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