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

2010/10/19 by Manfred G. Madritsch, Madritsch, Manfred G., Attila PethHö +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1010.3928

17 pages

arxiv created 2010/10/19 · arxiv updated 2010/10/20

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 Kátai to number systems defined in a quotient ring of the ring of polynomials over the integers.

Related

• The normality of digits in almost constant additive functions
• An estimate of asymptotics of the moments of additive arithmetic functions with a limit distribution defined on a subset of the natural series
• The distribution of sums and products of additive functions
• Additive bases arising from functions in a Hardy field
• Asymptotic behavior "almost everywhere" of additive and multiplicative arithmetic functions