Characterizations of additive functions

Laohakosol, Vichian; Tangsupphathawat, Pinthira

doi:10.1007/s10986-016-9333-0

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L-additive Functions In Terms Of the Dirichlet Convolution1

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2018

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“…Further properties of L-additive functions in terms of the Dirichlet convolution can be derived from the results in [11,8]. It would be possible to obtain some properties of L-additive functions in terms of the unitary convolution as well from the results in [8].…”

Section: L-additive Functions In Terms Of the Dirichlet Convolutionmentioning

confidence: 99%

The arithmetic derivative and Leibniz-additive functions

Haukkanen¹,

Merikoski²,

Tossavainen³

2018

NNTDM

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An arithmetic function f is Leibniz-additive if there is a completely multiplicative function h f , i.e., h f (1) = 1 and h f (mn) = h f (m)h f (n) for all positive integers m and n, satisfyingfor all positive integers m and n. A motivation for the present study is the fact that Leibniz-additive functions are generalizations of the arithmetic derivative D; namely, D is Leibniz-additive with h D (n) = n. In this paper, we study the basic properties of Leibniz-additive functions and, among other things, show that a Leibniz-additive function f is totally determined by the values of f and h f at primes. We also consider properties of Leibniz-additive functions with respect to the usual product, composition and Dirichlet convolution of arithmetic functions.

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Section: L-additive Functions In Terms Of the Dirichlet Convolutionmentioning

confidence: 99%