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arXiv · 2411.06126

On the error term concerning the number of cyclic subgroups of Z_l \times Z_m \times Z_n with lmn\leqslant x

Jing Ma·Jiaming Li·Jia Zhang
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Abstract

Let Zn denote the additive group of residue classes modulo n. Let c(l,m,n) denote the number of cyclic subgroups of Zl *Zm *Zn. For any x > 1, we consider the asymptotic behavior of D3c(x):= \sum_{lmn\leq x} c(l,m,n), obtain an asymptotic formula by complex method, and get an upper bound for the integral mean-square of the error term in that asymptotic formula.

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Jing Ma, Jiaming Li, Jia Zhang. 2024-11-09. On the error term concerning the number of cyclic subgroups of Z_l \times Z_m \times Z_n with lmn\leqslant x. https://arxiv.org/abs/2411.06126

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