The evaluation of two-dimensional lattice sums via Ramanujan's theta functions
Acta Arithmetica (2014)
- Volume: 165, Issue: 1, page 57-89
- ISSN: 0065-1036
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topPing Xu. "The evaluation of two-dimensional lattice sums via Ramanujan's theta functions." Acta Arithmetica 165.1 (2014): 57-89. <http://eudml.org/doc/279465>.
@article{PingXu2014,
abstract = {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.},
author = {Ping Xu},
journal = {Acta Arithmetica},
keywords = {two-dimensional lattice sums; Ramanujan's theta functions; continued fractions; class invariants; singular moduli; Poisson equation},
language = {eng},
number = {1},
pages = {57-89},
title = {The evaluation of two-dimensional lattice sums via Ramanujan's theta functions},
url = {http://eudml.org/doc/279465},
volume = {165},
year = {2014},
}
TY - JOUR
AU - Ping Xu
TI - The evaluation of two-dimensional lattice sums via Ramanujan's theta functions
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 1
SP - 57
EP - 89
AB - 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.
LA - eng
KW - two-dimensional lattice sums; Ramanujan's theta functions; continued fractions; class invariants; singular moduli; Poisson equation
UR - http://eudml.org/doc/279465
ER -
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