The sum of divisors of a quadratic form

Lilu Zhao. "The sum of divisors of a quadratic form." Acta Arithmetica 163.2 (2014): 161-177. <http://eudml.org/doc/279170>.

@article{LiluZhao2014,
abstract = {We study the sum τ of divisors of the quadratic form m₁² + m₂² + m₃². Let $S₃(X) = ∑_\{1≤m₁,m₂,m₃≤X\} τ(m₁²+m₂²+m₃²)$. We obtain the asymptotic formula S₃(X) = C₁X³logX + C₂X³ + O(X²log⁷X), where C₁,C₂ are two constants. This improves upon the error term $O_ε(X^\{8/3+ε\})$ obtained by Guo and Zhai (2012).},
author = {Lilu Zhao},
journal = {Acta Arithmetica},
keywords = {divisor function; quadratic form; Hardy-Littlewood-Kloosterman method},
language = {eng},
number = {2},
pages = {161-177},
title = {The sum of divisors of a quadratic form},
url = {http://eudml.org/doc/279170},
volume = {163},
year = {2014},
}

TY - JOUR
AU - Lilu Zhao
TI - The sum of divisors of a quadratic form
JO - Acta Arithmetica
PY - 2014
VL - 163
IS - 2
SP - 161
EP - 177
AB - We study the sum τ of divisors of the quadratic form m₁² + m₂² + m₃². Let $S₃(X) = ∑_{1≤m₁,m₂,m₃≤X} τ(m₁²+m₂²+m₃²)$. We obtain the asymptotic formula S₃(X) = C₁X³logX + C₂X³ + O(X²log⁷X), where C₁,C₂ are two constants. This improves upon the error term $O_ε(X^{8/3+ε})$ obtained by Guo and Zhai (2012).
LA - eng
KW - divisor function; quadratic form; Hardy-Littlewood-Kloosterman method
UR - http://eudml.org/doc/279170
ER -