# The moments of b-additive functions in canonical number systems

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The aim of the present paper is the estimation of the dth moment of additive functions in canonical number systems. These number systems are generalizations of the decimal number system to arbitrary polynomials having integer coefficients. We call a function additive (with respect to a number system) if it only acts on the digits of an expansion. The sum-ofdigits function, as a special additive function, has been analyzed in the case of q-adic number systems by Delange and number systems in number fields by Gittenberger and Thuswaldner. The present paper is a generalization of these results to arbitrary additive functions in canonical number systems. All rights reserved

Original language English 403-418 16 Acta Scientiarum Mathematicarum 78 3-4 Published - 2012

### Fingerprint

Canonical number System
Numbering systems
Number system
Moment
Decimal number
Arbitrary
Special Functions
Digit
Number field
Polynomial
Integer
Coefficient
Polynomials

### Keywords

• Canonical number systems
• Moment function

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics

### Cite this

The moments of b-additive functions in canonical number systems. / Madritsch, Manfred G.; Pethő, A.

In: Acta Scientiarum Mathematicarum, Vol. 78, No. 3-4, 2012, p. 403-418.

Research output: Contribution to journalArticle

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