An integer-valued multiplicative function f is said to be
polynomially-defined if there is a nonconstant separable polynomial F(T)βZ[T] with f(p)=F(p) for all primes p. We study the distribution
in coprime residue classes of polynomially-defined multiplicative functions,
establishing equidistribution results allowing a wide range of uniformity in
the modulus q. For example, we show that the values Ο(n), sampled over
integers nβ€x with Ο(n) coprime to q, are asymptotically
equidistributed among the coprime classes modulo q, uniformly for moduli q
coprime to 6 that are bounded by a fixed power of logx.Comment: edited paragraph following Theorem 1.3, correcting a claim in the
discussion of condition (i