Characterizing Completely Multiplicative Polynomial-Arithmetic Functions by Generalized M¨obius Functions

Narakorn Rompurk Kanasri

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Narakorn Rompurk Kanasri

Keywords:

polynomial-arithmetic function, complete multiplicativity, generalized M¨obius function

Abstract

Let $gif.latex?\Omega$ denote the set of monic polynomials over a finite field and let $gif.latex?A(\Omega)$ be the ring of arithmetic functions $gif.latex?f:\Omega\rightarrow\mathbb{C}$ . We construct a generalized M¨obius functions in $gif.latex?A(\Omega)$ and use it to characterize completely multiplicative functions in $gif.latex?A(\Omega)$ .

Characterizing Completely Multiplicative Polynomial-Arithmetic Functions by Generalized M¨obius Functions

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