38 citations · 115 across the 39 of their papers we have counts for
4 papers · 2 filters
Uncertainty principles connected with the Möbius inversion formula
Paul Pollack, Carlo Sanna
We say that two arithmetic functions f and g form a Mobius pair if f(n) = \sum_{d \mid n} g(d) for all natural numbers n. In that case, g can be expressed in terms of f by the fami…
Averages of the number of points on elliptic curves
Greg Martin, Paul Pollack, Ethan Smith
If is an elliptic curve defined over and is a prime of good reduction for , let denote the set of points on the reduced curve modulo . De…
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 $\D_F(n)$…
Practical pretenders
Paul Pollack, Lola Thompson
Following Srinivasan, an integer n\geq 1 is called practical if every natural number in [1,n] can be written as a sum of distinct divisors of n. This motivates us to define f(n) as…