Geodesic
The evaluation of two-dimensional lattice sums via Ramanujan's theta functions
Ping Xu1
1 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801, U.S.A. and 439 Cambridge St. Apt 23 Allston, MA 02134, U.S.A.
Acta Arithmetica, Tome 165 (2014) no. 1, pp. 57-89

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa165-1-4
Keywords: analyze various generalized two dimensional lattice sums which arose solution certain poisson equation evaluate certain lattice sums closed form using results ramanujans theory theta functions continued fractions class invariants many explicit examples given

Ping Xu 1

1 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801, U.S.A. and 439 Cambridge St. Apt 23 Allston, MA 02134, U.S.A. 
@article{10_4064_aa165_1_4,
     author = {Ping Xu},
     title = {The evaluation of two-dimensional lattice sums via
 {Ramanujan's} theta functions},
     journal = {Acta Arithmetica},
     pages = {57--89},
     publisher = {mathdoc},
     volume = {165},
     number = {1},
     year = {2014},
     doi = {10.4064/aa165-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa165-1-4/}
}
TY  - JOUR
AU  - Ping Xu
TI  - The evaluation of two-dimensional lattice sums via
 Ramanujan's theta functions
JO  - Acta Arithmetica
PY  - 2014
SP  - 57
EP  - 89
VL  - 165
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa165-1-4/
DO  - 10.4064/aa165-1-4
LA  - en
ID  - 10_4064_aa165_1_4
ER  - 
%0 Journal Article
%A Ping Xu
%T The evaluation of two-dimensional lattice sums via
 Ramanujan's theta functions
%J Acta Arithmetica
%D 2014
%P 57-89
%V 165
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa165-1-4/
%R 10.4064/aa165-1-4
%G en
%F 10_4064_aa165_1_4
Ping Xu. The evaluation of two-dimensional lattice sums via
 Ramanujan's theta functions. Acta Arithmetica, Tome 165 (2014) no. 1, pp. 57-89. doi: 10.4064/aa165-1-4

Cité par Sources :