On the derivative of anticyclotomic p-adic L-functions for Hilbert modular forms

Abstract

We construct anticyclotomic [Formula: see text]-adic [Formula: see text]-functions for ordinary Hilbert modular forms and a formula relating the first derivative of this [Formula: see text]-adic [Formula: see text]-function at the central point and Teieltbaum’s [Formula: see text]-invariant defined by Chida, Mok and Park. Our results extend previous works of Bertolini, Darmon, Iovita and Speiss to Hilbert modular forms of parallel weight [Formula: see text].