Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_{n+1} \times U_{n}$

Xenia Dimitrakopoulou

Published 2023-12-10Version 1

By $p$-adically interpolating the branching law for the spherical pair $(U_n, U_{n+1} \times U_{n})$ over an imaginary quadratic field, we construct a $p$-adic $L$-function attached to Coleman families of cohomological automorphic representations of $U_{n+1} \times U_{n}$. Our $p$-adic $L$-function interpolates the square root of the central critical $L$-value. It has weight and anticyclotomic variables and its construction relies on the proof of the unitary Gan--Gross--Prasad conjecture.