Extended arithmetic functions
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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.
KeywordsArithmetic functions Convolution product Idempotent
Mathematics Subject Classification11A25 16U99
The authors would like to thank the referee for his valuable comments which helped to improve the paper.
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