Joint distribution in residue classes of polynomial-like multiplicative functions

Paul Pollack, Akash Singha Roy

Published 2021-05-26Version 1

Under fairly general conditions, we show that families of integer-valued polynomial-like multiplicative functions are uniformly distributed in coprime residue classes mod $p$, where $p$ is a growing prime (or nearly prime) modulus. This can be seen as complementary to work of Narkiewicz, who obtained comprehensive results for fixed moduli.