A Polya-Vinogradov-type inequality on $\mathbb{Z}[i]$

TL;DR

This paper extends the classical Polya-Vinogradov inequality to the setting of Gaussian integers, providing bounds for character sums over this complex integer domain.

Contribution

It introduces a Polya-Vinogradov-type inequality specifically for multiplicative characters on the Gaussian integers, a novel extension of classical bounds.

Findings

Established a new bound for character sums over 

Extended classical inequalities to complex quadratic integer rings

Provides tools for analytic number theory in 

Abstract

We establish a Polya-Vinogradov-type bound for finite periodic multipicative characters on the Gaussian integers.