  Since the logarithm function is the solution of Poisson's equation in two
dimensions, it appears as the Coulomb interaction in two dimensions, the
interaction between Abrikosov flux lines in a type II superconductor, or
between line defects in elastic media, and so on. Lattices of lines interacting
logarithmically are, therefore, a subject of intense research due to their
manifold applications. The solution of the Poisson equation for such lattices
is known in the form of an infinite sum since the late 1990's. In this article
we present an alternative analytical solution, in closed form, in terms of the
Jacobi theta function.
