Asymptotic normality of b-additive functions on polynomial sequences in the Gaussian number field

[摘要] We consider the asymptotic behavior of h-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. (C) 2000 Academic Press.

[发布日期] 2000-10-01