We use hyperbolic geometry to study the limiting behavior of the average number of ways of expressing a number as the sum of two coprime squares. An alternative viewpoint using analytic number theory is also given.
@article{urn:eudml:doc:41295, title = {Expressing a number as the sum of two coprime squares.}, journal = {Collectanea Mathematica}, volume = {49}, year = {1998}, pages = {283-291}, zbl = {0926.11023}, mrnumber = {MR1677144}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41295} }
Dicks, Warren; Porti, Joan. Expressing a number as the sum of two coprime squares.. Collectanea Mathematica, Tome 49 (1998) pp. 283-291. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41295/