Work

Some Perpendicularities of Arithmetical Functions

Year: 2025

Type: article

Abstract: We introduce the notion of perpendicularity of arithmetical functions and discuss a few concrete examples of perpendicularities. Further, we show that the set of arithmetical functions f with f(1) = 1 forms a real vector space with the Dirichlet convolution as addition and real power under the Dirichlet convolution as scalar multiplication. Moreover, we prove that multiplicative functions are perpendicular to antimultiplicative functions with respect to the natural perpendicularity.

Source: KTH Publication Database DiVA (KTH Royal Institute of Technology)

DOI: 10.5281/zenodo.15283661

Authors: Haukkanen, Pentti, Tossavainen, Timo

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6912246186

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