The evaluation of two-dimensional lattice sums via Ramanujan's theta functions
Volume 165 / 2014
Acta Arithmetica 165 (2014), 57-89 MSC: Primary 33E05; Secondary 11F27, 35J05. DOI: 10.4064/aa165-1-4
We analyze various generalized two-dimensional lattice sums, one of which arose from the solution to a certain Poisson equation. We evaluate certain lattice sums in closed form using results from Ramanujan's theory of theta functions, continued fractions and class invariants. Many explicit examples are given.