Paul Pollack

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20142023

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5 papers · 1 filter

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…

math.NT2016

The truth about torsion in the CM case, II

Pete L. Clark, Paul Pollack

Let $T_{CM} (d)$ be the largest size of the torsion subgroup of an elliptic curve with complex multiplication (CM) defined over a degree $d$ number field. Work of Breuer and Cla…

math.NT2014

Bounded gaps between primes with a given primitive root, II

Roger C. Baker, Paul Pollack

Let $m$ be a natural number, and let $Q$ be a set containing at least $exp (C m)$ primes. We show that one can find infinitely many strings of $m$ consecutive primes each…