The arithmetic function ρ(n) counts the number of ways to write a positive integer n as a difference of two squares. Its average size is described by the Dirichlet summatory function Σn≤x ρ(n), and in particular by the error term R(x) in the corresponding asymptotics. This article provides a sharp lower bound as well as two mean-square results for R(x), which illustrates the close connection between ρ(n) and the number-of-divisors function d(n).
@article{bwmeta1.element.doi-10_1007_s11533-005-0007-0,
author = {Manfred K\"uhleitner and Werner Nowak},
title = {On differences of two squares},
journal = {Open Mathematics},
volume = {4},
year = {2006},
pages = {110-122},
zbl = {1146.11048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0007-0}
}
Manfred Kühleitner; Werner Nowak. On differences of two squares. Open Mathematics, Tome 4 (2006) pp. 110-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0007-0/
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