in 1978, katz gave a construction of the $p$-adic $l$-function of a cm field by using a $p$-adic analog of the maass--shimura operators acting on $p$-adic hilbert modular forms. however, this $p$-adic maass--shimura operator is only defined over the ordinary locus, which restricted katz's choice of $p$ to one that splits in the cm field. in 2021, andreatta and iovita extended katz's construction to all $p$ for quadratic imaginary fields using overconvergent differential operators constructed by harron--xiao and urban, which act on elliptic modular forms. here we give a construction of such overconvergent differential operators which act on hilbert modular forms.

[pre-talk at 1:20pm]