On q-Quasiadditive and q-Quasimultiplicative Functions
Date
2017
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Electronic Journal of Combinatorics
Abstract
In this paper, we introduce the notion of q-quasiadditivity of arithmetic functions,
as well as the related concept of q-quasimultiplicativity, which generalise
strong q-additivity and -multiplicativity, respectively. We show that there are many
natural examples for these concepts, which are characterised by functional equations
of the form f(qk+ra+b) = f(a)+f(b) or f(qk+ra+b) = f(a)f(b) for all b < qk and a
fixed parameter r. In addition to some elementary properties of q-quasiadditive and
q-quasimultiplicative functions, we prove characterisations of q-quasiadditivity and
q-quasimultiplicativity for the special class of q-regular functions. The final main
result provides a general central limit theorem that includes both classical and new
examples as corollaries.
Description
CITATION: Kropf, S. & Wagner, S. 2017. On q-Quasiadditive and q-Quasimultiplicative Functions. Electronic Journal of Combinatorics, 24(1):1-22.
The original publication is available at https://www.combinatorics.org/ojs/index.php/eljc
The original publication is available at https://www.combinatorics.org/ojs/index.php/eljc
Keywords
Regular functions, Central limit theorem, Additive functions, Quasi-additive functions
Citation
Kropf, S. & Wagner, S. 2017. On q-Quasiadditive and q-Quasimultiplicative Functions. Electronic Journal of Combinatorics, 24(1):1-22