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arxiv: 2606.07785 · v1 · pith:UPFUI6FAnew · submitted 2026-06-05 · 🧮 math.NT · math.CA

Explicit bounds for Dickman's function

classification 🧮 math.NT math.CA
keywords boundsdickmanexplicitfunctionnumericallyallowsapproximatedelay
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We establish numerically explicit upper and lower bounds for Dickman's function $\rho(u)$, 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 $\rho(u)$ without the need to solve the delay differential equation numerically.

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