Average values of quadratic Hecke character sums

TL;DR

This paper investigates smoothed quadratic Hecke character sums over Gaussian integers, extending existing results to broader ranges and providing asymptotic formulas for these sums.

Contribution

It introduces new asymptotic formulas for quadratic Hecke character sums over larger ranges of variables, expanding the understanding of these sums in the Gaussian field.

Findings

Derived asymptotic formulas for quadratic Hecke character sums

Extended known results to larger ranges of summation variables

Enhanced understanding of character sum behavior in Gaussian integers

Abstract

We study smoothed character sums involving $\sum_{m,n} ( \frac{m}{n} )_2$, where $( \frac{m}{n} )_2$ denotes the quadratic symbol in the Gaussian field. We extend previously known results to obtain asymptotic formulas for the sums considered to larger ranges of $m$ and $n$.