Asymptotics of the Discrete Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice

We consider the Hamiltonian $H_\mu(K)$ of a system consisting of three bosons that interact through attractive pair contact potentials on a three-dimensional integer lattice. We obtain an asymptotic value for the number $N(K,z)$ of eigenvalues of the operator $H_{\mu_0}(K)$ lying below $z\le0$ with respect to the total quasimomentum $K\to0$ and the spectral parameter $z\to-0$.