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A Notion of Positive Definiteness for Arithmetical Functions

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Original languageEnglish
Title of host publicationMatrices, Statistics and Big Data
Subtitle of host publicationSelected Contributions from IWMS 2016
EditorsS. Ejaz Ahmed, Francisco Carvalho, Simo Puntanen
PublisherSpringer Nature
Number of pages14
ISBN (Electronic)978-3-030-17519-1
ISBN (Print)978-3-030-17518-4
Publication statusPublished - 2019
Publication typeA4 Article in a conference publication
EventInternational Workshop on Matrices and Statistics - Funchal, Portugal
Duration: 6 Jun 20169 Jun 2016
Conference number: 25

Publication series

NameContributions to Statistics
ISSN (Print)1431-1968


ConferenceInternational Workshop on Matrices and Statistics
Abbreviated titleIWMS


In the theory of Fourier transform some functions are said to be positive definite based on the positive definiteness property of a certain class of matrices associated with these functions. In the present article we consider how to define a similar positive definiteness property for arithmetical functions, whose domain is not the set of real numbers but merely the set of positive integers. After finding a suitable definition for this concept we shall use it to construct a partial ordering on the set of arithmetical functions. We shall study some of the basic properties of our newly defined relations and consider a couple of well-known arithmetical functions as examples.

Publication forum classification

Field of science, Statistics Finland