Some aspects of number theory related to phase operators
Functional Analysis
2018-12-27 v2 Mathematical Physics
math.MP
Operator Algebras
Abstract
We first extend the multiplicativity property of arithmetic functions to the setting of operators on the Fock space. Secondly, we use phase operators to get representation of some extended arithmetic functions by operators on the Hardy space. Finally, we show that radial limits to the boundary of the unit disc in the Hardy space is useful in order to go back to the classical arithmetic functions. Our approach can be understudied as a transition from the classical number theory to quantum setting.
Cite
@article{arxiv.1812.03486,
title = {Some aspects of number theory related to phase operators},
author = {F. Bouzeffour and M. Garayev},
journal= {arXiv preprint arXiv:1812.03486},
year = {2018}
}
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