Trace formulae for Schr\"odinger operators with complex-valued   potentials on cubic lattices
  We consider Schr\"odinger operators with complex decaying potentials on the lattice. Using some classical results from Complex Analysis we obtain some trace formulae and using them estimate globally all zeros of the Fredholm determinant in terms of the potential. 
Evgeny Korotyaev, Ari Laptev
math.SP