A Formula of the Dirichlet Character Sum

TL;DR

This paper introduces a new formula for calculating Dirichlet character sums using Fourier series expansion, supported by four specific examples demonstrating its application.

Contribution

It provides a novel formula for Dirichlet character sums based on Fourier series, enhancing computational methods in number theory.

Findings

Derived a formula for Dirichlet character sums

Presented four illustrative examples

Improves computational techniques in number theory

Abstract

In this paper, We use the Fourier series expansion of real variables function, We give a formula to calculate the Dirichlet character sum, and four special examples are given.