# Some generalizations of the functions $\tau$ and $\tau^{\left(e\right)}$ in algebraic number fields

## TL;DR

This paper extends the definitions of the arithmetic functions  and ^{(e)} in algebraic number fields and explores their properties, contributing to the theoretical understanding of these functions in algebraic number theory.

## Contribution

The paper introduces generalized versions of  and ^{(e)} in algebraic number fields and analyzes their properties, expanding the theoretical framework of these functions.

## Key findings

- Generalized  and ^{(e)} functions in algebraic number fields.
- Derived properties of the generalized functions.
- Enhanced understanding of arithmetic functions in algebraic number theory.

## Abstract

In this paper, we generalize the arithmetic functions $\tau$ and $\tau^{\left(e\right)}$ in algebraic number fields and we find some properties of these functions.