Browsing University of Waterloo by Author "Elma, Ertan"

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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 ...
Some Problems in Multiplicative and Additive Number Theory

Elma, Ertan (University of Waterloo, 2020-07-27)

In this thesis, we obtain several results in number theory. Let $k\geqslant 1$ be a natural number and $\omega_k(n)$ denote the number of distinct prime factors of a natural number $n$ with multiplicity $k$. We estimate ...