The evaluation of two-dimensional lattice sums via Ramanujan's theta functions
Ping Xu
Acta Arithmetica, Tome 166 (2014), p. 57-89 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:279465 
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     title = {The evaluation of two-dimensional lattice sums via Ramanujan's theta functions},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {57-89},
     zbl = {06345772},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-1-4}
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Ping Xu. The evaluation of two-dimensional lattice sums via Ramanujan's theta functions. Acta Arithmetica, Tome 166 (2014) pp. 57-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-1-4/