Geodesic
The sum of divisors of a quadratic form
Lilu Zhao 1
1 School of Mathematics Hefei University of Technology Hefei 230009, People's Republic of China
Acta Arithmetica, Tome 163 (2014) no. 2, pp. 161-177 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the sum $\tau$ of divisors of the quadratic form $m_1^2+m_2^2+m_3^2$. Let $$S_3(X)=\sum_{1\le m_1,m_2,m_3\le X}\tau(m_1^2+m_2^2+m_3^2).$$ We obtain the asymptotic formula $$S_3(X)=C_1X^3\log X+ C_2X^3+O(X^2\log^7 X),$$ where $C_1,C_2$ are two constants. This improves upon the error term $O_\varepsilon(X^{8/3+\varepsilon})$ obtained by Guo and Zhai (2012).
DOI : 10.4064/aa163-2-6
Keywords: study sum tau divisors quadratic form sum tau obtain asymptotic formula log log where constants improves error term varepsilon varepsilon obtained guo zhai

Lilu Zhao  1

1 School of Mathematics Hefei University of Technology Hefei 230009, People's Republic of China 
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Lilu Zhao. The sum of divisors of a quadratic form. Acta Arithmetica, Tome 163 (2014) no. 2, pp. 161-177. doi: 10.4064/aa163-2-6

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