Geodesic
An asymptotic formula related to the sums of divisors
Meng Zhang1
1 School of Mathematics and Quantitative Economics Shandong University of Finance and Economics 40 Shungeng Road Jinan, Shandong 250014, P.R. China
Acta Arithmetica, Tome 175 (2016) no. 2, pp. 183-200.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $d(n)$ be the number of divisors of $n$, and $k$ a positive integer. It is proved that the sum $\sum_{1\leq m_1,\dots,m_s\leq X}d(m_1^k+\cdots+m_s^k)$ has an asymptotic formula for $k\geq2$ and $s \gt \min\{2^{k-1}, k^2+k-2\}.$
DOI : 10.4064/aa8391-5-2016
Keywords: number divisors positive integer proved sum sum leq dots leq cdots has asymptotic formula geq min k k

Meng Zhang 1

1 School of Mathematics and Quantitative Economics Shandong University of Finance and Economics 40 Shungeng Road Jinan, Shandong 250014, P.R. China 
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Meng Zhang. An asymptotic formula related to the sums of divisors. Acta Arithmetica, Tome 175 (2016) no. 2, pp. 183-200. doi : 10.4064/aa8391-5-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8391-5-2016/

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