SOME LOGARITHMIC LATTICE SUMS

In this paper we consider certain lattice sums which arise when a syst em of line charges set in a compensating jelly of opposite charge inte ract via the two-dimensional logarithmic potential. A lattice-limit di scontinuity phenomenon, similar to that discovered by Borwein et al in the three-dimensional case, is explored and a high-precision asymptot ic method is described for the numerical computation of two-dimensiona l lattice limits.