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Complex Analysis and Operator Theory

, Volume 12, Issue 7, pp 1567–1608 | Cite as

Correction: An Application of Free Probability to Arithmetic Functions

  • Ilwoo Cho
  • Palle E. T. Jorgensen
Article
  • 69 Downloads

Abstract

In this paper, we study free probability on tensor product algebra \(\mathfrak {M} = M\,\otimes _{\mathbb {C}}\,{\mathcal {A}}\) of a \(W^{*}\)-algebra M and the algebra \({\mathcal {A}}\), consisting of all arithmetic functions equipped with the functional addition and the convolution. We study free-distributional data of certain elements of \(\mathfrak {M}\), and study freeness on \(\mathfrak {M}\), affected by fixed primes.

Keywords

Free probability Free moments Free cumulants Arithmetic functions The arithmetic algebra \({\mathcal {A}}\) Tensor product 

Mathematics Subject Classification

05E15 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 47L15 47L30 47L55 

Notes

Acknowledgements

The authors sincerely apologize to the readers, and they hope this corrected version will be a chance to help fixing their mistakes with apology. The authors found mistakes in Sects. 4 and 5 in the original published paper thanks to Prof. Brent Nelson, who indicated the mistakes which the corresponding author made. The authors specially thank Prof. Nelson for his kind indication and opinions. Also, the authors apologize to the editors of the journal, Compl. Anal. Oper. Theo.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSt. Ambrose UniversityDavenportUSA
  2. 2.Department of Mathematics and StatisticsUniversity of IowaIowa CityUSA

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