A Polya-Vinogradov-type inequality on $\mathbb{Z}[i]$
Number Theory
2017-03-29 v2
Abstract
We establish a Polya-Vinogradov-type bound for finite periodic multipicative characters on the Gaussian integers.
Cite
@article{arxiv.1703.06498,
title = {A Polya-Vinogradov-type inequality on $\mathbb{Z}[i]$},
author = {Stephan Baier},
journal= {arXiv preprint arXiv:1703.06498},
year = {2017}
}
Comments
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