The sum of divisors of a quadratic form
Lilu Zhao
Acta Arithmetica, Tome 166 (2014), p. 161-177 / Harvested from The Polish Digital Mathematics Library
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We study the sum τ of divisors of the quadratic form m₁² + m₂² + m₃². Let S₃(X)=∑1≤m₁,m₂,m₃≤Xτ(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 Oε(X8/3+ε) obtained by Guo and Zhai (2012).

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:279170 
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     title = {The sum of divisors of a quadratic form},
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     volume = {166},
     year = {2014},
     pages = {161-177},
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     language = {en},
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Lilu Zhao. The sum of divisors of a quadratic form. Acta Arithmetica, Tome 166 (2014) pp. 161-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-2-6/