Mean values of some Hecke characters
Volume 187 / 2019
Acta Arithmetica 187 (2019), 125-141
MSC: 11L05, 11L40, 11R11.
DOI: 10.4064/aa170827-9-3
Published online: 14 November 2018
Abstract
We evaluate a smoothed character sum involving $\newcommand{\bleg}[2]{\big(\frac{#1}{#2}\big)}\sum_{m}\sum_{n}\bleg {m}{n}$, where $\newcommand{\bleg}[2]{\big(\frac{#1}{#2}\big)}\bleg{m}{n}$ is a quadratic, cubic or quartic Hecke character, and the two sums over $m$ and $n$ are of comparable lengths.
