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arXiv · 2305.07658

Global numerical bounds for the number-theoretic omega functions

Mehdi Hassani
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Abstract

We obtain global explicit numerical bounds, with best possible constants, for the differences $\frac{1}{n}\sum_{k\leq n}\omega(k)-\log\log n$ and$ \frac{1}{n}\sum_{k\leq n}\Omega(k)-\log\log n$, where $\omega(k)$ and $\Omega(k)$ refer to the number of distinct prime divisors, and the total number of prime divisors of $k$, respectively.

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Mehdi Hassani. 2023-04-09. Global numerical bounds for the number-theoretic omega functions. https://arxiv.org/abs/2305.07658

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