Extended arithmetic functions

  • Fethi BouzeffourEmail author
  • Wissem Jedidi
  • Mubariz Garayev


In this paper, we give an attempt to extend some arithmetic properties such as multiplicativity and convolution products to the setting of operator theory and we provide significant examples which are of interest in number theory. We also give a representation of the Euler differential operator by means of the Euler totient arithmetic function and idempotent elements of some associative unital algebra.


Arithmetic functions Convolution product Idempotent 

Mathematics Subject Classification

11A25 16U99 



The authors would like to thank the referee for his valuable comments which helped to improve the paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Fethi Bouzeffour
    • 1
    • 2
    Email author
  • Wissem Jedidi
    • 3
    • 4
  • Mubariz Garayev
    • 1
  1. 1.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia
  2. 2.University of CarthageJarzounaTunisia
  3. 3.Department of Statistics & ORKing Saud UniversityRiyadhSaudi Arabia
  4. 4.Université de Tunis El Manar, Faculté des Sciences de Tunis, LR11ES11 Laboratoire d’Analyse Mathématiques et ApplicationsTunisTunisia

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