Displaying similar documents to “Banach algebra techniques in the theory of arithmetic functions”

On certain arithmetic functions involving the greatest common divisor

Ekkehard Krätzel, Werner Nowak, László Tóth (2012)

Open Mathematics

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The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.

A note on ( a , b ) -Fibonacci sequences and specially multiplicative arithmetic functions

Emil Daniel Schwab, Gabriela Schwab (2024)

Mathematica Bohemica

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A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely ( a , b ) -Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly. ...