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- W4360979968 abstract "An integer-valued multiplicative function f is said to be polynomially-defined if there is a nonconstant separable polynomial $$F(T)in mathbb {Z}[T]$$ 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 $$phi (n)$$ , sampled over integers $$n le x$$ with $$phi (n)$$ 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 $$log {x}$$ ." @default.
- W4360979968 created "2023-03-30" @default.
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- W4360979968 date "2023-03-17" @default.
- W4360979968 modified "2023-09-28" @default.
- W4360979968 title "Distribution in coprime residue classes of polynomially-defined multiplicative functions" @default.
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- W4360979968 doi "https://doi.org/10.1007/s00209-023-03240-7" @default.
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