A. Roy

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math.NT2022

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 $k$ -divisor functions, where $k \neq = 1 0^{j}$ ,…

math.NT2021

Powerfree sums of proper divisors

Paul Pollack, Akash Singha Roy

Let $s (n) := \sum_{d ∣ n, d < n} d$ denote the sum of the proper divisors of $n$ . It is natural to conjecture that for each integer $k \geq 2$ , the equivalence \[ \text{ $n$ is $k$ th p…

math.NT2021

Distribution mod $p$ 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 $p$ of Euler's totient function $ϕ (n)$ and the sum-of-proper-divisors function $s (n) := σ (n) - n$ . We prove that the value…

math.NT2021

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 $p$ , wher…

On Benford's Law for multiplicative functions

Powerfree sums of proper divisors

Distribution mod p of Euler's totient and the sum of proper divisors

Joint distribution in residue classes of polynomial-like multiplicative functions

Distribution mod $p$ of Euler's totient and the sum of proper divisors