# Sums over Vanishing Determinants

## TL;DR

This paper investigates sums of arithmetic functions over Gaussian integers, focusing on pairs that form singular systems, and explores their properties and implications.

## Contribution

It introduces a novel analysis of sums over Gaussian integers constrained by singular systems, expanding understanding of their arithmetic behavior.

## Key findings

- Derived new bounds for sums over Gaussian integers
- Identified conditions for singular systems in Gaussian integer pairs
- Extended classical results to complex integer domains

## Abstract

We study sums of arithmetic functions, defined on Gaussian integers and taken over those pairs of integers whose coordinates give rise to a singular system.