Geodesic
On the Davison Convolution of Arithmetical Functions
Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 467-473

Voir la notice de l'article provenant de la source Cambridge University Press

The Davison convolution of arithmetical functions f and g is defined by where K is a complex-valued function on the set of all ordered pairs (n, d) such that n is a positive integer and d is a positive divisor of n. In this paper we shall consider the arithmetical equations f(r) = g, f(r) = fg, f o g = h in f and the congruence (f o g)(n) = 0 (mod n), where f(r) is the iterate of f with respect to the Davison convolution.
DOI : 10.4153/CMB-1989-067-4
Mots-clés : 10A20 
Haukkanen, Pentti. On the Davison Convolution of Arithmetical Functions. Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 467-473. doi: 10.4153/CMB-1989-067-4
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[1] 1. Carlitz, L. and M. V. Subbarao, Transformation of arithmetic functions, Duke Math J. 40 (1973), 949–958. Google Scholar

[2] 2. Cohen, E., Arithmetical functions associated with the unitary divisors of an integer, Math. Z. 74 (1960), 66–80. Google Scholar

[3] 3. Davison, T. M. K., On arithmetic convolutions, Canad. Math. Bull. 9 (1966), 287–296. Google Scholar

[4] 4. Ferrero, M., On generalized convolution rings of arithmetic functions, Tsukuba J. Math. 4 (1980), 161–176. Google Scholar

[5] 5. Fotino, LP., Generalized convolution ring of arithmetic functions, Pacific J. Math. 61 (1975), 103– 116. Google Scholar

[6] 6. Fredman, M. L., Arithmetical convolution products, Duke Math J. 37 (1970), 231–242. Google Scholar

[7] 7. Gessley, M. D., A generalized arithmetic convolution, Amer. Math. Monthly 74 (1967), 1216–1217. Google Scholar

[8] 8. Gioia, A. A., The K-product of arithmetic functions, Canad. J. Math. 17 (1965), 970–976. Google Scholar

[9] 9. Gioia, A. A. and M. Subbarao, V., Generalized Dirichlet products of arithmetic functions (Abstract), Notices Amer. Math. Soc. 9 (1962), 305. Google Scholar

[10] 10. Hanumanthachari, J., On an arithmetic convolution, Canad. Math. Bull. 20 (1977), 301–305. Google Scholar

[11] 11. Haukkanen, P., Arithmetical equations involving semi-multiplicative functions and the Dirichlet product (To appear in Rend. Math.). Google Scholar

[12] 12. Lahiri, D. B., Hypo-multiplicative number-theoretic functions, Aequationes Math. 9 (1973), 184–192. Google Scholar

[13] 13. McCarthy, P. J., Note on some arithmetic sums, Boll. Un. Mat. Ital. 21 (1966), 239–242. Google Scholar

[14] 14. McCarthy, P. J., Introduction to arithmetical functions, Springer, 1986. Google Scholar

[15] 15. Narkiewicz, W., On a class of arithmetical convolutions, Colloq. Math. 10 (1963), 81–94. Google Scholar

[16] 16. Rearick, D., Semi-multiplicative functions, Duke Math. J. 33 (1966), 49–53. Google Scholar

[17] 17. Subbarao, M. V., A congruence for a class of arithmetic functions, Canad. Math. Bull. 9 (1966), 571–574. Google Scholar

[18] 18. Subbarao, M. V., A class of arithmetical equations, Nieuw Arch. Wisk. 15 (1967), 211–217. Google Scholar

[19] 19. Yocom, K. L., Totally multiplicative functions in regular convolution rings, Canad. Math. Bull. 16 (1973), 119–129. Google Scholar

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