%0 Journal Article %T Modified wave operators for discrete Schr£żdinger operators with long-range perturbations %A Shu Nakamura %J Mathematics %D 2014 %I arXiv %X We consider the scattering theory for discrete Schr\"odinger operators on $Z^d$ with long-range potentials. We prove the existence of modified wave operators constructed in terms of solutions of a Hamilton-Jacobi equation on the torus $T^d$. %U http://arxiv.org/abs/1403.2795v1