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 Tóth; Wenguang Zhai

doi:10.4064/aa171111-7-2

¹Department of Mathematics University of Pécs Ifjúság útja 6 H-7624 Pécs, Hungary
²Department of Mathematics China University of Mining and Technology Beijing 100083, P.R. China

Acta Arithmetica, Tome 183 (2018) no. 3, pp. 285-299

Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Résumé

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

Affiliations des auteurs :

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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     title = {On the error term concerning the number of subgroups of the groups $\mathbb {Z}_m \times \mathbb {Z}_n$ with $m,n\le x$},
     journal = {Acta Arithmetica},
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     year = {2018},
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     doi = {10.4064/aa171111-7-2},
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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

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