Browsing Waterloo Research by Author "Elma, Ertan"
Now showing items 1-2 of 2
-
Number of prime factors with a given multiplicity
Elma, Ertan; Liu, Yu-Ru (Cambridge University Press, 2022-03)Let k ⩾ 1 be a natural number and ωk (n) denote the number of distinct prime factors of a natural number n with multiplicity k. We estimate the first and second moments of the functions ωk with k ⩾ 1. Moreover, we prove ... -
On the number of irreducible factors with a given multiplicity in function fields
Das, Sourabhashis; Elma, Ertan; Kuo, Wentang; Liu, Yu-Ru (Elsevier, 2023-12)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 ...