P. Pollack

activity

20092026

most citedBounded gaps between primes with a given primitive root

38 citations · 115 across the 39 of their papers we have counts for

collaborators

56 papers

math.NT2026

Amicable numbers

Paul Pollack

Let $s (n) := \sum_{d ∣ n, d < n} d$ denote the sum of the proper divisors of $n$ . Distinct positive integers $n, m$ form an amicable pair if $s (n) = m$ and $s (m) = n$ . Let $A (x)$ count…

math.NT2026

On the digits of the sum of proper divisors

Kübra Benli, Cécile Dartyge, Charlotte Dombrowsky +2

We study several probabilistic questions concerning the digits of $s (n)$ , the sum of proper divisors of an integer $n$ . In particular, we show that $s (n)$ obeys Benford's law with…

math.NT2026

Small values of Carmichael's lambda function

Paul Pollack

Let $λ (n)$ be the exponent of the multiplicative group $(Z / n Z)^{\times}$ , and set $L (x, y) = # {n \leq x : λ (n) \leq y}$ . We prove an upper bound for $\log \frac{L(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.NT2023

Densities of integer sets represented by quadratic forms

Pete L. Clark, Paul Pollack, Jeremy Rouse +1

Let $f (t_{1}, \dots, t_{n})$ be a nondegenerate integral quadratic form. We analyze the asymptotic behavior of the function $D_{f} (X)$ , the number of integers of absolute value up to $X$ …

math.NT2023

Two problems on the distribution of Carmichael's lambda function

Paul Pollack

Let $λ (n)$ denote the exponent of the multiplicative group modulo $n$ . We show that when $q$ is odd, each coprime residue class modulo $q$ is hit equally often by $λ (n)$ as $n$ var…