Matthew Just

most citedOn upper bounds for the count of elite primes

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math.NT2025

Partition-theoretic model of prime distribution

Aidan Botkin, Madeline L. Dawsey, David J. Hemmer +2

We make an application of ideas from partition theory to a problem in multiplicative number theory. We propose a deterministic model of prime number distribution, from first princi…

math.NT2021

A "supernormal" partition statistic

Madeline Locus Dawsey, Matthew Just, Robert Schneider

We study a bijective map from integer partitions to the prime factorizations of integers that we call the "supernorm" of a partition, in which the multiplicities of the parts of pa…

math.NT2021

Numbers which are only orders of abelian or nilpotent groups

Matthew Just

Refining a result of Erdos and Mays, we give asymptotic series expansions for the functions $A (x) - C (x)$ , the count of $n \leq x$ for which every group of order $n$ is abelian (but n…

math.NT2021

On factorizations into coprime parts

Matthew Just, Noah Lebowitz-Lockard

Let $f (n)$ and $g (n)$ be the number of unordered and ordered factorizations of $n$ into integers larger than one. Let $F (n)$ and $G (n)$ have the additional restriction that the fac…

math.NT2021★ 1 cited

On upper bounds for the count of elite primes

Matthew Just

We look at upper bounds for the count of certain primes related to the Fermat numbers $F_{n} = 2^{2^{n}} + 1$ called elite primes. We first note an oversight in a result of Krizek, Luca an…

math.NT2021★ 1 cited

Variations on a theme of Schinzel and Wójcik

Matthew Just, Paul Pollack

Schinzel and Wójcik have shown that if $α, β$ are rational numbers not $0$ or $\pm 1$ , then $ord_{p} (α) = ord_{p} (β)$ for infinitely many primes $p$ , where $\mathrm{ord…