# Mean values of cubic and quartic Dirichlet Characters

## TL;DR

This paper computes the average sums of cubic and quartic Dirichlet characters for large moduli, extending previous work on quadratic characters to higher powers.

## Contribution

It generalizes existing results on quadratic characters to cubic and quartic cases, providing new average value formulas for these higher-power Dirichlet characters.

## Key findings

- Derived explicit formulas for average sums of cubic and quartic Dirichlet characters.
- Extended previous quadratic character results to higher-power characters.
- Analyzed the behavior of character sums for large moduli.

## Abstract

We evaluate the average of cubic and quartic Dirichlet character sums with the modulus going up to a size comparable to the length of the individual sums. This generalizes a result of Conrey, Farmer and Soundararajan on quadratic Dirichlet character sums.