Greg Martin

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math.NT2024

Multiplicative groups avoiding a fixed group

Matthias Hannesson, Greg Martin

We know that any finite abelian group $G$ appears as a subgroup of infinitely many multiplicative groups $Z_{n}^{\times}$ (the abelian groups of size $I ¨ (n)$ that are the mult…

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…