=== CORRECTION There is a mistake in formula (3.3) of the paper P.G. Martinsson, G.J.Rodin "Boundary Algebraic Equations for Lattice Problems" Proceedings of the Royal Society A, 465(2108), pp. 2489-2503, 2009. The equation should read $$ G(m) = -(\log|m| + \gamma + (\log 8)/2)/(2\pi) + O(|m|^{-2}), $$ where $\gamma = 0.5772...$ is the Euler constant. A correct account can be found in P.G. Martinsson, G. Rodin, "Asymptotic expansions of lattice Green's functions". Proceedings of the Royal Society A, 458, 2002, pp. 2609--2622. Many thanks to Igor Tsukerman of the University of Akron for pointing this issue out to us.