Functional equation of the $p$-adic $L$-function of Bianchi modular forms

Abstract

Let $K$ be an imaginary quadratic field with class number 1, in this paper we obtain the functional equation of the $p$-adic $L$-function of small slope $p$-stabilised Bianchi modular forms. Then, using $p$-adic families of Bianchi modular forms, we extend our result to $\hat{I}\pounds$-smooth base-change Bianchi modular forms.

Final version