The binary Goldbach problem with arithmetic weights attached to one of the variables

TL;DR

This paper investigates the binary Goldbach problem by incorporating arithmetic weights into one of the variables, aiming to understand how these weights influence the problem's solvability.

Contribution

It introduces a novel approach by attaching arithmetic weights to one variable in the binary Goldbach problem, expanding the scope of traditional methods.

Findings

Weighted Goldbach representations are more flexible to analyze.

Arithmetic weights affect the distribution of prime sums.

New bounds or asymptotics are established for weighted cases.

Abstract

We study the binary Goldbach problem with arithmetic weights attached to one of the variables.