Logarithmic interaction under periodic boundary conditions: closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results J. Math. Phys., 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler J. Math. Phys., 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation.