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Pollack, Paul; Singha Roy, Akash
Mathematische Zeitschrift, 04/2023, Letnik: 303, Številka: 4Journal Article
An integer-valued multiplicative function f is said to be polynomially-defined if there is a nonconstant separable polynomial F ( T ) ∈ Z 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 ϕ ( n ) , sampled over integers n ≤ x with ϕ ( 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 log x .
