Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Note on arithmetic convolution equations


Author: Michal Feckan
Journal: Proc. Amer. Math. Soc. 136 (2008), 453-459
MSC (2000): Primary 11A25
DOI: https://doi.org/10.1090/S0002-9939-07-09162-9
Published electronically: November 2, 2007
MathSciNet review: 2358483
Full-text PDF

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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] T. CARROLL AND A. A. GIOIA: Roots of multiplicative functions, Compositio Mat. 65 (1988), 349-358. MR 932075 (89c:11007)
  • [3] M. J. COHEN: Advanced problem 5293, Amer. Math. Monthly 72 (1965), 555; Solution, ibid 73 (1966), 553-554.
  • [4] P.-O. DEHAYE: On the structure of the group of multiplicative arithmetical functions, Bull. Belgian Math. Soc. 9 (2002), 15-21. MR 1905645 (2003d:11009)
  • [5] J. GLÖCKNER, L. G. LUCHT AND Š. PORUBSKÝ: Solutions to arithmetic convolution equations, Proc. Amer. Math. Soc., to appear. MR 2286069
  • [6] 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)
  • [7] P. HEWITT AND J. H. WILLIAMSON: Note on absolutely convergent Dirichlet series, Proc. Amer. Math. Soc. 8 (1957), 863-868. MR 0090680 (19:851b)
  • [8] 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)
  • [9] M. V. SUBBARAO: A class of arithmetical functions, Nieuw Archief voor Wiskunde (3) 15 (1967), 211-217. MR 0223293 (36:6341)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11A25

Retrieve articles in all journals with MSC (2000): 11A25


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, Štefánikova 49, 814 73 Bratislava, Slovakia
Email: Michal.Feckan@fmph.uniba.sk

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

American Mathematical Society