Nathan McNew

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20222024

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math.NT2023

Short Interval Results For Powerfree Polynomials Over Finite Fields

Angel Kumchev, Nathan McNew, Ariana Park

Let $k \geq 2$ be an integer and $F_{q}$ be a finite field with $q$ elements. We prove several results on the distribution in short intervals of polynomials in $\mathbb F_q[x…

math.NT2023

The distribution of intermediate prime factors

Nathan McNew, Paul Pollack, Akash Singha Roy

Let $P^{(\frac{1}{2})} (n)$ denote the middle prime factor of $n$ (taking into account multiplicity). More generally, one can consider, for any $α \in (0, 1)$ , the $α$ -positio…

math.NT2022

Permutations and the divisor graph of $[1, n]$

Nathan McNew

Let $S_{div} (n)$ denote the set of permutations $π$ of $n$ such that for each $1 \leq j \leq n$ either $j ∣ π (j)$ or $π (j) ∣ j$ . These permutations can also be viewed as v…

Short Interval Results For Powerfree Polynomials Over Finite Fields

The distribution of intermediate prime factors

Permutations and the divisor graph of [1,n]

Permutations and the divisor graph of $[1, n]$