Title: A general method for calculating lattice Green functions on the branch cut,
Abstract: We present a method for calculating the complex Green function $G_{ij}
(\omega)$ at any real frequency $\omega$ between any two sites $i$ and $j$ on a
lattice. Starting from numbers of walks on square, cubic, honeycomb,
triangular, bcc, fcc, and diamond lattices, we derive Chebyshev expansion
coefficients for $G_{ij} (\omega)$. The convergence of the Chebyshev series can
be accelerated by constructing functions $f(\omega)$ that mimic the van Hove
singularities in $G_{ij} (\omega)$ and subtracting their Chebyshev coefficients
from the original coefficients. We demonstrate this explicitly for the square
lattice and bcc lattice. Our algorithm achieves typical accuracies of 6--9
significant figures using 1000 series terms.