Greg Martin

collaborators

3 papers

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 $ϕ (n)$ that are the multi…

math.NT2024

Distribution of the number of prime factors with a given multiplicity

Ertan Elma, Greg Martin

Given an integer $k \geq 2$ , let $ω_{k} (n)$ 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 $…

math.NT2024

The least primary factor of the multiplicative group

Greg Martin, Chau Nguyen

Let $S (n)$ denote the least primary factor in the primary decomposition of the multiplicative group $M_{n} = (Z / n Z)^{\times}$ . We give an asymptotic formula, with order of ma…