# On differences of two squares

Manfred Kühleitner; Werner Nowak

Open Mathematics (2006)

- Volume: 4, Issue: 1, page 110-122
- ISSN: 2391-5455

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topManfred Kühleitner, and Werner Nowak. "On differences of two squares." Open Mathematics 4.1 (2006): 110-122. <http://eudml.org/doc/268724>.

@article{ManfredKühleitner2006,

abstract = {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).},

author = {Manfred Kühleitner, Werner Nowak},

journal = {Open Mathematics},

keywords = {11N37},

language = {eng},

number = {1},

pages = {110-122},

title = {On differences of two squares},

url = {http://eudml.org/doc/268724},

volume = {4},

year = {2006},

}

TY - JOUR

AU - Manfred Kühleitner

AU - Werner Nowak

TI - On differences of two squares

JO - Open Mathematics

PY - 2006

VL - 4

IS - 1

SP - 110

EP - 122

AB - 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).

LA - eng

KW - 11N37

UR - http://eudml.org/doc/268724

ER -

## References

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