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The evaluation of two-dimensional lattice sums via Ramanujan's theta functions

Ping Xu (2014)

Acta Arithmetica

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.

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