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

TL;DR

This paper investigates the asymptotic distribution of digit-based functions in polynomial-based number systems, extending previous results to more general algebraic structures.

Contribution

It generalizes the asymptotic normality results for digit functions to polynomial quotient rings, broadening the scope of prior work.

Findings

Established asymptotic normality for digit functions in polynomial quotient rings

Extended previous results from integer-based systems to algebraic polynomial systems

Provided a theoretical framework for analyzing digit functions in complex number systems

Abstract

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.