Wang, Boying; Hou, Yaoping Multi-extension of arithmetic functions and its applications. (English) Zbl 0921.11006 J. Math. Study 30, No. 3, 226-230 (1997). Let \(f\) be an arithmetic function. The authors define the gcd-extensions of \(f\) (these are arithmetic functions in several variables) and generalize Smith’s determinant. The proofs are elementary. Reviewer: J.Spilker (Freiburg i.Br.) MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11C20 Matrices, determinants in number theory Keywords:gcd-extensions of an arithmetic function; arithmetic functions in several variables; Smith’s determinant PDFBibTeX XMLCite \textit{B. Wang} and \textit{Y. Hou}, J. Math. Study 30, No. 3, 226--230 (1997; Zbl 0921.11006)