Joint distribution in residue classes of polynomial-like multiplicative functions

TL;DR

This paper proves that polynomial-like multiplicative functions are uniformly distributed across coprime residue classes modulo large primes, extending previous fixed-moduli results to growing prime moduli.

Contribution

It establishes uniform distribution results for polynomial-like multiplicative functions in residue classes modulo large primes, complementing prior fixed-moduli studies.

Findings

Families of such functions are uniformly distributed in coprime residue classes mod p

Distribution holds under fairly general conditions

Results extend to growing prime or nearly prime moduli

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.