Extended arithmetic functions

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Abstract

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.

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Acknowledgements

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

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Correspondence to Fethi Bouzeffour.

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Fethi Bouzeffour and Mubariz Garayev would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this research through the Research Group No. RGP-VPP-323.

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Bouzeffour, F., Jedidi, W. & Garayev, M. Extended arithmetic functions. Ramanujan J 51, 593–609 (2020). https://doi.org/10.1007/s11139-018-0122-8

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Keywords

  • Arithmetic functions
  • Convolution product
  • Idempotent

Mathematics Subject Classification

  • 11A25
  • 16U99