Note on arithmetic convolution equations

Fečkan, Michal

doi:10.1090/S0002-9939-07-09162-9

Note on arithmetic convolution equations
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by Michal Fečkan

Proc. Amer. Math. Soc. 136 (2008), 453-459

DOI: https://doi.org/10.1090/S0002-9939-07-09162-9

Published electronically: November 2, 2007

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Abstract:

We investigate the solvability of polynomial equations on the $\mathbb C$-algebra of arithmetic functions $g : \mathbb N\to \mathbb C$.

References

H. Biller: Analyticity and naturality of the multi-variable functional calculus, TU Darmstadt Preprint 2332, 2004; http:wwwbib.mathematik.tu-darmstadt.de/Math-Net /Preprints/Listen/files/2332.ps.gz.
Tim Carroll and A. A. Gioia, Roots of multiplicative functions, Compositio Math. 65 (1988), no. 3, 349–358. MR 932075
M. J. Cohen: Advanced problem 5293, Amer. Math. Monthly 72 (1965), 555; Solution, ibid 73 (1966), 553-554.
Paul-Olivier Dehaye, On the structure of the group of multiplicative arithmetical functions, Bull. Belg. Math. Soc. Simon Stevin 9 (2002), no. 1, 15–21. MR 1905645
Helge Glöckner, Lutz G. Lucht, and Štefan Porubský, Solutions to arithmetic convolution equations, Proc. Amer. Math. Soc. 135 (2007), no. 6, 1619–1629. MR 2286069, DOI 10.1090/S0002-9939-07-08738-2
P. Haukkanen, Arithmetical equations involving semi-multiplicative functions and the Dirichlet convolution, Rend. Mat. Appl. (7) 8 (1988), no. 4, 511–517 (1989) (English, with Italian summary). MR 1032719
Edwin Hewitt and J. H. Williamson, Note on absolutely convergent Dirichlet series, Proc. Amer. Math. Soc. 8 (1957), 863–868. MR 90680, DOI 10.1090/S0002-9939-1957-0090680-X
Štefan Porubský, Structure of the group of quasi multiplicative arithmetical functions, Acta Acad. Paedagog. Agriensis Sect. Math. (N.S.) 30 (2003), 133–145. Dedicated to the memory of Professor Dr. Péter Kiss. MR 2054723
M. V. Subbarao, A class of arithmetical equations, Nieuw Arch. Wisk. (3) 15 (1967), 211–217. MR 223293