On Robin's Inequality and the Kaneko-Lagarias Inequality
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909738236641280 |
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| author | Assani, Idris Chester, Aiden Paschal, Alex |
| author_facet | Assani, Idris Chester, Aiden Paschal, Alex |
| contents | We provide new, elementary proofs that Robin's inequality and the Lagarias inequality hold for almost every number, including all numbers not divisible by one of the prime numbers $2$, $3$, $5$; all primorials; given $k$ a natural number, all sufficiently large numbers of the form $2^kn$ for $n\ge1$ odd; and all $21$-free integers. Additionally, we prove that the Kaneko-Lagarias inequality holds for all natural numbers if and only if it holds for all superabundant numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Robin's Inequality and the Kaneko-Lagarias Inequality Assani, Idris Chester, Aiden Paschal, Alex Number Theory 11M26, 11N56 We provide new, elementary proofs that Robin's inequality and the Lagarias inequality hold for almost every number, including all numbers not divisible by one of the prime numbers $2$, $3$, $5$; all primorials; given $k$ a natural number, all sufficiently large numbers of the form $2^kn$ for $n\ge1$ odd; and all $21$-free integers. Additionally, we prove that the Kaneko-Lagarias inequality holds for all natural numbers if and only if it holds for all superabundant numbers. |
| title | On Robin's Inequality and the Kaneko-Lagarias Inequality |
| topic | Number Theory 11M26, 11N56 |
| url | https://arxiv.org/abs/2503.03159 |