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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.21757 |
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| _version_ | 1866909807062024192 |
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| author | Luo, Yongbing Yan, Ping |
| author_facet | Luo, Yongbing Yan, Ping |
| contents | This paper proves a conjecture proposed by Ren and Li (2015: 393, \emph{Journal of Inequalities and Applications}). Our result eliminates the constraints on the parity and size of $m$, as well as the restriction $x > 1$, required in Ren and Li's theorem. Consequently, it fully subsumes their results while extending validity to all integers $m \geq 1$ and all $x > 0$. Crucially, we establish the inequality $S_m(x) > σ_m(x)$ unconditionally, requiring no parity conditions, size conditions on $m$, or lower bound on $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Conjecture by Ren and Li Luo, Yongbing Yan, Ping Classical Analysis and ODEs This paper proves a conjecture proposed by Ren and Li (2015: 393, \emph{Journal of Inequalities and Applications}). Our result eliminates the constraints on the parity and size of $m$, as well as the restriction $x > 1$, required in Ren and Li's theorem. Consequently, it fully subsumes their results while extending validity to all integers $m \geq 1$ and all $x > 0$. Crucially, we establish the inequality $S_m(x) > σ_m(x)$ unconditionally, requiring no parity conditions, size conditions on $m$, or lower bound on $x$. |
| title | On a Conjecture by Ren and Li |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.21757 |