Geodesic
An asymptotic formula related to the sums of divisors
Meng Zhang1
1School 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

DOI

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 
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
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