On the error term concerning the number of cyclic subgroups of Z_l \times Z_m \times Z_n with lmn\leqslant x
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929586080579584 |
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| author | Ma, Jing Li, Jiaming Zhang, Jia |
| author_facet | Ma, Jing Li, Jiaming Zhang, Jia |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_06126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the error term concerning the number of cyclic subgroups of Z_l \times Z_m \times Z_n with lmn\leqslant x Ma, Jing Li, Jiaming Zhang, Jia Number Theory 11Axx Elementary number theory G.0 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. |
| title | On the error term concerning the number of cyclic subgroups of Z_l \times Z_m \times Z_n with lmn\leqslant x |
| topic | Number Theory 11Axx Elementary number theory G.0 |
| url | https://arxiv.org/abs/2411.06126 |