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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Note on arithmetic convolution equations

Author(s): Michal Feckan
Journal: Proc. Amer. Math. Soc. 136 (2008), 453-459.
MSC (2000): Primary 11A25
Posted: November 2, 2007
MathSciNet review: 2358483
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Abstract | References | Similar articles | Additional information

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


References:

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T. CARROLL AND A. A. GIOIA: Roots of multiplicative functions, Compositio Mat. 65 (1988), 349-358. MR 932075 (89c:11007)

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J. GLÖCKNER, L. G. LUCHT AND Š. PORUBSKÝ: Solutions to arithmetic convolution equations, Proc. Amer. Math. Soc., to appear. MR 2286069

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P. HAUKKANEN: Arithmetical equations involving semi-multiplicative functions and the Dirichlet convolution, Rend. Mat. Appl., VII. Ser. 8 (1988), 511-517. MR 1032719 (90k:11007)

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P. HEWITT AND J. H. WILLIAMSON: Note on absolutely convergent Dirichlet series, Proc. Amer. Math. Soc. 8 (1957), 863-868. MR 0090680 (19:851b)

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Š. PORUBSKÝ: Structure of the group of quasi-multiplicative arithmetical functions, Acta Arith. Paed. Agiensis, Sect. Math. 30 (2003), 133-145. MR 2054723 (2005b:11006)

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Additional Information:

Michal Feckan
Affiliation: Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia; and Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73 Bratislava, Slovakia
Email: Michal.Feckan@fmph.uniba.sk

DOI: 10.1090/S0002-9939-07-09162-9
PII: S 0002-9939(07)09162-9
Keywords: Arithmetic functions, Dirichlet convolution
Received by editor(s): December 1, 2006
Posted: November 2, 2007
Additional Notes: This work was supported by the Grant VEGA-SAV 2/7140/27.
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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