# Gaussian primes in almost all narrow sectors

## TL;DR

This paper investigates the distribution of Gaussian primes within narrow sectors of the complex plane, demonstrating that almost all such sectors contain the expected number of primes when the sectors are sufficiently wide.

## Contribution

It establishes that almost all narrow sectors, above a certain width, contain the expected number of Gaussian primes, advancing understanding of their distribution in the complex plane.

## Key findings

- Almost all sectors above a certain width contain the expected primes.
- Distribution of Gaussian primes aligns with probabilistic predictions in narrow sectors.
- Results hold for sectors that are not too narrow.

## Abstract

We study Gaussian primes lying in narrow sectors, and show that almost all such sectors contain the expected number of primes, if the sectors are not too narrow.