Asymptotic normality of additive functions on polynomial sequences in canonical number systems

The objective of this paper is the study of functions which only act on the digits of an expansion. In particular, we are interested in the asymptotic distribution of the values of these functions. The presented result is an extension and generalization of a result of Bassily and K\'atai to number systems defined in a quotient ring of the ring of polynomials over the integers.Comment: 17 page

Construction of normal numbers via pseudo-polynomial prime sequences

In the present paper we construct normal numbers in base $q$ by concatenating $q$-ary expansions of pseudo polynomials evaluated at the primes. This extends a recent result by Tichy and the author