Asymptotic Normality of b-Additive Functions on Polynomial Sequences in the Gaussian Number Field, Original Research Article

We consider the asymptotic behavior of b-additive functions f with respect to a base b of a canonical number system in the Gaussian number field. In particular, we get a normal limit law for f(P(z)) where P(z) is a polynomial with integer coefficients. Our methods are exponential sums over the Gaussian number field as well as certain results from the theory of uniform distribution.