Electron-phonon interaction near Van Hove singularities

The Eliashberg equations are solved in two dimensions for the transition temperature of a superconductor. The density of states has a logarithmic singularity. We show that the singularity in the density of states has only a small influence on the numerical solutions to the Eliashberg equations, apart from its contributions to the electron-phonon interaction {λ}. We also consider the effects of the angular dependence of the gap around the Fermi line which occur for s-wave pairing.