Five-variable $p$-adic $L$-functions for $U(3)\times U(2)$

Abstract

We construct a five-variable $p$-adic $L$-function attached to Hida families on the definite unitary groups $U(3)$ and $U(2)$ by using the Ichino-Ikeda formula. The interpolation formula fits into the conjectural shape of $p$-adic $L$-functions predicted by Coates and Perrin-Riou.