5 citations · 12 across the 6 of their papers we have counts for
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Distribution in coprime residue classes of polynomially-defined multiplicative functions
Paul Pollack, Akash Singha Roy
An integer-valued multiplicative function is said to be polynomially-defined if there is a nonconstant separable polynomial with for all pri…
Two problems concerning irreducible elements in rings of integers of number fields
Paul Pollack, Lee Troupe
Let be a number field with ring of integers . We prove two asymptotic formulas connected with the distribution of irreducible elements in . First, w…
Besicovitch, Bisection, and the normality of
Paul Pollack, Joseph Vandehey
We revisit Besicovitch's 1935 paper in which he introduced several techniques that have become essential elements of modern combinatorial methods of normality proofs. Despite his p…
Arithmetic functions at consecutive shifted primes
Paul Pollack, Lola Thompson
For each of the functions and every natural number , we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots…
Bounded gaps between primes in number fields and function fields
Abel Castillo, Chris Hall, Robert J. Lemke Oliver +2
The Hardy--Littlewood prime -tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs…
On the degrees of divisors of T^n-1
Paul Pollack, Lola Thompson
Fix a field . In this paper, we study the sets $\D_F(n) \subset [0,n]$ defined by [\D_F(n):= {0 \leq m \leq n: T^n-1\text{has a divisor of degree in} F[T]}.] When $\D_F(n)$…