Geodesic
On the error term concerning the number of subgroups of the groups $\mathbb {Z}_m \times \mathbb {Z}_n$ with $m,n\le x$
László Tóth1 ; Wenguang Zhai2
1 Department of Mathematics University of Pécs Ifjúság útja 6 H-7624 Pécs, Hungary
2 Department of Mathematics China University of Mining and Technology Beijing 100083, P.R. China
Acta Arithmetica, Tome 183 (2018) no. 3, pp. 285-299.

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

Let $\mathbb{Z}_{m}$ be the additive group of residue classes modulo $m$. Let $s(m,n)$ and $c(m,n)$ denote the total number of subgroups and the number of cyclic subgroups of the group $\mathbb{Z}_{m}\times \mathbb{Z}_{n}$, respectively, where $m$ and $n$ are arbitrary positive integers. W. G. Nowak and L. Tóth (2014) investigated the asymptotic behavior of the sums $\sum_{m,n\leq x} s(m,n)$ and $\sum_{m,n\leq x} c(m,n)$. We improve the error terms of these asymptotic formulas.
DOI : 10.4064/aa171111-7-2
Keywords: mathbb additive group residue classes modulo denote total number subgroups number cyclic subgroups group mathbb times mathbb respectively where arbitrary positive integers nbsp nbsp nowak nbsp investigated asymptotic behavior sums sum leq sum leq improve error terms these asymptotic formulas

László Tóth 1 ; Wenguang Zhai 2

1 Department of Mathematics University of Pécs Ifjúság útja 6 H-7624 Pécs, Hungary
2 Department of Mathematics China University of Mining and Technology Beijing 100083, P.R. China 
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László Tóth; Wenguang Zhai. On the error term concerning the number of subgroups of the groups $\mathbb {Z}_m \times \mathbb {Z}_n$ with $m,n\le x$. Acta Arithmetica, Tome 183 (2018) no. 3, pp. 285-299. doi : 10.4064/aa171111-7-2. http://geodesic.mathdoc.fr/articles/10.4064/aa171111-7-2/

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