On a class of ψ-convolutions characterized by the identical equation
Journal de Théorie des Nombres de Bordeaux, Volume 14 (2002) no. 2, pp. 561-583.

The identical equation for multiplicative functions established by R. Vaidyanathaswamy in the case of Dirichlet convolution in 1931 has been generalized to multiplicativity preserving ψ-convolutions satisfying certain conditions (cf. [7]) which can be called as Lehmer-Narkiewicz convolutions for some reasons. In this paper we prove the converse.

Dans le cadre de la convolution de Dirichlet des fonctions arithmétiques, R. Vaidyanathaswamy a obtenu en 1931 une formule de calcul de f(mn) valable pour toute fonction multiplicative f et tout couple d’entiers positifs m et n. Dans [7], cette formule a été généralisée aux ψ-convolutions appelées convolutions de Lehmer-Narkiewicz, qui, entre autres, conservent la multiplicativité. Dans cet article, nous démontrons la réciproque.

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Jean-Louis Nicolas; Varanasi Sitaramaiah. On a class of $\psi $-convolutions characterized by the identical equation. Journal de Théorie des Nombres de Bordeaux, Volume 14 (2002) no. 2, pp. 561-583. doi : 10.5802/jtnb.375. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.375/

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