# On the $L^1$ norm of an exponential sum involving the divisor function

## TL;DR

This paper derives bounds on the $L^1$ norm of exponential sums involving the divisor function, contributing to understanding their size and behavior in analytic number theory.

## Contribution

It provides new bounds on the $L^1$ norm of exponential sums with the divisor function, advancing previous results in the field.

## Key findings

- Established explicit bounds on the $L^1$ norm for the sum involving $ au(n)$
- Improved understanding of the sum's growth and oscillation
- Potential applications to problems in analytic number theory

## Abstract

In this paper, we obtain bounds on the $L^1$ norm of the sum $\sum_{n\le x}\tau(n) e(\alpha n)$ where $\tau(n)$ is the divisor function.