The exceptional zero conjecture for Hilbert modular forms

Abstract

AbstractUsing ap-adic analogue of the convolution method of Rankin–Selberg and Shimura, we construct the two-variablep-adicL-function of a Hida family of Hilbert modular eigenforms of parallel weight. It is shown that the conditions of Greenberg–Stevens [R. Greenberg and G. Stevens,p-adic L-functions and p-adic periods of modular forms, Invent. Math.111(1993), 407–447] are satisfied, from which we deduce special cases of the Mazur–Tate–Teitelbaum conjecture in the Hilbert modular setting.