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

Abstract

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

This result has been proved in stronger and much more general form by E. Landau using Hecke L-functions, which escaped my attention. However, the main part of the method in my article consists of refined estimates for averages of linear exponential sums on Z[i] over regions. These estimates have other applications, and I will provide one soon in a new paper