# Some aspects of number theory related to phase operators

## TL;DR

This paper explores the connection between number theory and quantum operators, extending classical arithmetic functions to the Fock space and Hardy space, and analyzing boundary limits to bridge to classical results.

## Contribution

It introduces a novel approach by extending multiplicativity to operators on Fock space and representing arithmetic functions via phase operators on Hardy space.

## Key findings

- Extended multiplicativity property to Fock space operators
- Representation of arithmetic functions using phase operators
- Radial limits in Hardy space help recover classical arithmetic functions

## 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.