Joint distribution in residue classes of polynomial-like multiplicative functions

Abstract

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.

13 pages; corrected an error in part (b) of the Remark following Lemma 2.2