P. Pollack

activity

20152026

most citedAnatomy of torsion in the CM case

3 citations · 6 across the 13 of their papers we have counts for

collaborators

Showing 2021Show all

6 papers · 1 filter

math.NT2021

A problem in comparative order theory

Sergei Konyagin, Paul Pollack

Write $ord_{p} (\cdot)$ for the multiplicative order in $F_{p}^{\times}$ . Recently, Matthew Just and the second author investigated the problem of classifying pairs $α…

math.NT2021

Powerfree sums of proper divisors

Paul Pollack, Akash Singha Roy

Let $s (n) := \sum_{d ∣ n, d < n} d$ denote the sum of the proper divisors of $n$ . It is natural to conjecture that for each integer $k \geq 2$ , the equivalence \[ \text{ $n$ is $k$ th p…

math.NT2021

Sums of proper divisors follow the Erdős--Kac law

Paul Pollack, Lee Troupe

Let $s (n) = \sum_{d ∣ n, d < n} d$ denote the sum of the proper divisors of $n$ . The second-named author proved that $ω (s (n))$ has normal order $lo g lo g n$ , the analogue for $s$ -va…

math.NT2021

Distribution mod $p$ of Euler's totient and the sum of proper divisors

Noah Lebowitz-Lockard, Paul Pollack, Akash Singha Roy

We consider the distribution in residue classes modulo primes $p$ of Euler's totient function $ϕ (n)$ and the sum-of-proper-divisors function $s (n) := σ (n) - n$ . We prove that the value…

math.NT2021

Joint distribution in residue classes of polynomial-like multiplicative functions

Paul Pollack, Akash Singha Roy

Under fairly general conditions, we show that families of integer-valued polynomial-like multiplicative functions are uniformly distributed in coprime residue classes mod $p$ , wher…

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…

A problem in comparative order theory

Powerfree sums of proper divisors

Sums of proper divisors follow the Erdős--Kac law

Distribution mod p of Euler's totient and the sum of proper divisors

Joint distribution in residue classes of polynomial-like multiplicative functions

Variations on a theme of Schinzel and Wójcik

Distribution mod $p$ of Euler's totient and the sum of proper divisors