Das, SourabhashisElma, ErtanKuo, WentangLiu, Yu-Ru2023-10-032023-10-032023-12https://doi.org/10.1016/j.ffa.2023.102281http://hdl.handle.net/10012/20009The final publication is available at Elsevier via https://doi.org/10.1016/j.ffa.2023.102281. © 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Let k ≥ 1 be a natural number and f ∈ Fq[t] be a monic polynomial. Let ωk(f) denote the number of distinct monic irreducible factors of f with multiplicity k. We obtain asymptotic estimates for the first and the second moments of ωk(f) with k ≥ 1. Moreover, we prove that the function ω1(f) has normal order log(deg(f)) and also satisfies the Erdős-Kac Theorem. Finally, we prove that the functions ωk(f) with k ≥ 2 do not have normal order.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/monic irreducible factorsnormal orderErdős-Kac theoremArticle