Year: 2026
Type: preprint
Abstract: Dickman's function $ρ(u)$ denotes the natural density of integers $n$ whose largest prime factor does not exceed $n^{1/u}$. We establish numerically explicit upper and lower bounds for $ρ(u)$, resulting in estimates with a relative error of less than $0.005/u^2$ for all $u\ge 5$. This allows for an approximate evaluation of $ρ(u)$ without the need to solve the delay differential equation numerically.
Source: arXiv (Cornell University)
Author: Weingartner, Andreas
Institution: Southern Utah University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164049034