Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates

Christina Giannitsi, Ben Krause, Michael Lacey +2

We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $\omega \subset \mathbb{T}$. There is an integer $N_{\omega }$, so that every odd integer $n$…