Year: 2026
Type: preprint
Abstract: For $κ> 1$, we study the reciprocal LCM-power function \[ σ^{[κ]}_{-1}(n) := \sum_{d \mid n}μ(d)\,σ_{-1}(n / d)^κ. \] We determine its average and extremal orders. A natural Robin-scale normalization is strictly increasing in $κ$ and tends to $σ_{-1}$, yielding an RH-equivalent criterion. Unconditionally, the corresponding Robin inequality holds eventually on every bounded parameter interval. Directed interval arithmetic proves the inequality for each $n > 5040$ and $1 < κ\le 100{,}000$.
Source: arXiv (Cornell University)
Author: Molnar, Grant
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221564321