Numerically explicit version of the P\'{o}lya--Vinogradov inequality

TL;DR

This paper presents a new explicit numerical version of the Pólya--Vinogradov inequality, improving previous bounds through innovative methods inspired by V.A. Bykovskii and C. Pomerance.

Contribution

It introduces a more precise explicit bound for the Pólya--Vinogradov inequality, advancing the understanding of character sum estimates.

Findings

Provides a numerically explicit bound for the inequality

Improves upon recent bounds by Pomerance

Utilizes new ideas from Bykovskii

Abstract

In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obtained by C. Pomerance.