Ertan Elma

collaborators

3 papers

math.NT2025

On the Second Hardy-Littlewood Conjecture

Bittu Chahal, Ertan Elma, Nic Fellini +2

The second Hardy-Littlewood conjecture asserts that the prime counting function $I ¨ (x)$ satisfies the subadditive inequality \begin{align*} Ï(x+y)\leqslant Ï(x)+Ï(y) \end{align*…

math.NT2024

On the number of irreducible factors with a given multiplicity in function fields

Sourabhashis Das, Ertan Elma, Wentang Kuo +1

Let $k \geq 1$ be a natural number and $f \in F_{q} [t]$ be a monic polynomial. Let $I ¨ _{k} (f)$ denote the number of distinct monic irreducible factors of $f$ with multiplicity…

math.NT2024

Distribution of the number of prime factors with a given multiplicity

Ertan Elma, Greg Martin

Given an integer $k \geq 2$ , let $I ¨ _{k} (n)$ denote the number of primes that divide $n$ with multiplicity exactly $k$ . We compute the density $e_{k, m}$ of those integers $n$ for which…