On differences of two squares

Manfred Kühleitner; Werner Nowak

Open Mathematics (2006)

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

Abstract

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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).

How to cite

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Manfred 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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