P. Pollack

activity

20152026

most citedAnatomy of torsion in the CM case

3 citations · 9 across the 14 of their papers we have counts for

collaborators

Showing 2020Show all

5 papers · 1 filter

math.NT2020

A quick route to unique factorization in quadratic orders

Paul Pollack, Noah Snyder

We give a short proof -- not relying on ideal classes or the geometry of numbers -- of a known criterion for quadratic orders to possess unique factorization.

math.NT2020

Numbers which are orders only of cyclic groups

Paul Pollack

We call $n$ a cyclic number if every group of order $n$ is cyclic. It is implicit in work of Dickson, and explicit in work of Szele, that $n$ is cyclic precisely when $\gcd(n,ϕ(n))…

math.NT2020

Finite sets containing near-primitive roots

Komal Agrawal, Paul Pollack

Fix $a \in Z$ , $a \in / {0, \pm 1}$ . A simple argument shows that for each $ε > 0$ , and almost all (asymptotically 100% of) primes $p$ , the multiplicative order of $a$ mod…

math.NT2020

The reciprocal sum of divisors of Mersenne numbers

Zebediah Engberg, Paul Pollack

We investigate various questions concerning the reciprocal sum of divisors, or prime divisors, of the Mersenne numbers $2^{n} - 1$ . Conditional on the Elliott-Halberstam Conjecture and…

math.NT2020

Phi, Primorials, and Poisson

Paul Pollack, Carl Pomerance

The primorial $p #$ of a prime $p$ is the product of all primes $q \leq p$ . Let pr $(n)$ denote the largest prime $p$ with $p # ∣ ϕ (n)$ , where $ϕ$ is Euler's totient function. We s…