arXiv subjects
Publications and source records attributed to Luis Santiago Palacios.
Let $K$ be an imaginary quadratic field. In this article, we construct $p$-adic $L$-functions of non-cuspidal Bianchi modular forms by introducing the notions of $C$-cuspidality and partial Bianchi modular symbols. When $p$ splits in $K$, we focus on $p$-adic $L$-functions of non-cuspidal base change Bianchi modular forms, showing that they factor as products of two Katz $p$-adic $L$-functions.
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 $Σ$-smooth base-change Bianchi modular forms.
Let $K$ be an imaginary quadratic field. In this article, we study the local geometry of the Bianchi eigenvariety around non-cuspidal classical points, in particular, ordinary non-cuspidal base change points. To perform this study we introduce Bianchi Eisenstein eigensystems and prove strong multiplicity-one results on the cohomology of the corresponding Bianchi threefolds. We believe these results are of independent interest.