Representation of even Gaussian integer \`a la Chen

TL;DR

This paper extends Chen's approach to Gaussian integers, showing that large even Gaussian integers can be expressed as a sum of a Gaussian prime and a Gaussian integer with limited prime factors.

Contribution

It introduces a novel representation of large even Gaussian integers, paralleling Chen's theorem in the rational integers.

Findings

Large even Gaussian integers can be expressed as a sum of a Gaussian prime and a Gaussian integer with at most two prime factors.

The representation holds for sufficiently large norms.

The method parallels Chen's theorem for rational integers.

Abstract

In this article, we represent an even Gaussian integer with sufficiently large norm as a sum of a Gaussian prime and a Gaussian integer with at most two Gaussian prime factors akin to Chen in the rational case.