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On q-Quasiadditive and q-Quasimultiplicative Functions

dc.contributor.authorKropf, Saraen_ZA
dc.contributor.authorWagner, Stephanen_ZA
dc.date.accessioned2018-08-23T11:12:42Z
dc.date.available2018-08-23T11:12:42Z
dc.date.issued2017
dc.identifier.citationKropf, S. & Wagner, S. 2017. On q-Quasiadditive and q-Quasimultiplicative Functions. Electronic Journal of Combinatorics, 24(1):1-22en_ZA
dc.identifier.issn1077-8926 (online)
dc.identifier.urihttp://hdl.handle.net/10019.1/104335
dc.descriptionCITATION: Kropf, S. & Wagner, S. 2017. On q-Quasiadditive and q-Quasimultiplicative Functions. Electronic Journal of Combinatorics, 24(1):1-22.en_ZA
dc.descriptionThe original publication is available at https://www.combinatorics.org/ojs/index.php/eljcen_ZA
dc.description.abstractIn 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.en_ZA
dc.description.urihttps://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i1p60
dc.format.extent22 pagesen_ZA
dc.language.isoen_ZAen_ZA
dc.publisherElectronic Journal of Combinatoricsen_ZA
dc.subjectRegular functionsen_ZA
dc.subjectCentral limit theoremen_ZA
dc.subjectAdditive functionsen_ZA
dc.subjectQuasi-additive functionsen_ZA
dc.titleOn q-Quasiadditive and q-Quasimultiplicative Functionsen_ZA
dc.typeArticleen_ZA
dc.description.versionPublisher's versionen_ZA
dc.rights.holderAuthors retain copyrighten_ZA


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