An asymptotic formula for Goldbach's conjecture with monic polynomials in $\mathbb{Z}[\theta ][x]$

Abílio Lemos, Anderson L. A. Araujo

In this paper, we consider $D=\mathbb{Z}[\theta ]$, where $$θ= \sqrt{-k} \,\,\,\, \mbox{if}\;\;\;-k\not\equiv 1 \;(\mbox{mod}\;4)\,\,\,\,\mbox{or}\,\,\,\, θ=\frac{\sqrt{-k}+1}{2} \,\,\,\…