Asymptotics of the discrete spectrum of a model operator associated with a system of three particles on a lattice

We consider a model Schrödinger operator $H_\mu$ associated with a system of three particles on the three-dimensional lattice $\mathbb Z^3$ with a functional parameter of special form. We prove that if the corresponding Friedrichs model has a zero-energy resonance, then the operator $H_\mu$ has infinitely many negative eigenvalues accumulating at zero (the Efimov effect). We obtain the asymptotic expression for the number of eigenvalues of $H_\mu$ below $z$ as $z\to-0$.