3 citations · 6 across the 8 of their papers we have counts for
21 papers · 1 filter
On Benford's Law for multiplicative functions
Vorrapan Chandee, Xiannan Li, Paul Pollack +1
We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the -divisor functions, where ,…
A problem in comparative order theory
Sergei Konyagin, Paul Pollack
Write for the multiplicative order in . Recently, Matthew Just and the second author investigated the problem of classifying pairs $α…
Powerfree sums of proper divisors
Paul Pollack, Akash Singha Roy
Let denote the sum of the proper divisors of . It is natural to conjecture that for each integer , the equivalence \[ \text{ is th p…
Sums of proper divisors follow the Erdős--Kac law
Paul Pollack, Lee Troupe
Let denote the sum of the proper divisors of . The second-named author proved that has normal order , the analogue for -va…
Distribution mod 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 of Euler's totient function and the sum-of-proper-divisors function . We prove that the value…
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 , wher…