Calogero-Moser eigenfunctions modulo $p^s$

In this note we use the Matsuo-Cherednik duality between the solutions to KZ equations and eigenfunctions of Calogero-Moser Hamiltonians to get the polynomial $p^s$-truncation of the Calogero-Moser eigenfunctions at a rational coupling constant. The truncation procedure uses the integral representation for the hypergeometric solutions to KZ equations. The $s\to \mathrm{\infty }$ limit to the pure $p$-adic case has been analyzed in the $n=2$ case