Separable expansions for virtual states and resonances

Finite rank expansions for two- and three-body $t$ matrices are analytically continued to the unphysical sheet of the complex energy plane associated with the lowest two-body scattering threshold in order to obtain the position and residue of the virtual state and resonance poles. The present method is applied to study the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ virtual state of two nucleons, the Efimov virtual states of three identical bosons, and the doublet virtual state of three nucleons.