Asymptotic normality of \(b\)-additive functions on polynomial sequences in the Gaussian number field (Q1590270)

The authors consider the asymptotic behaviour of \(b\)-additive functions \(f\) with respect to a base \(b\) of a canonical number system in the Gaussian number field. In particular, a normal limit law for \(f (P(z))\) is proved, where \(P(z)\) is a polynomial with integer coefficients. The proofs depend on methods from the theory of exponential sums and on results from the theory of uniform distribution.