On the Distribution of Primes in an Imaginary Quadratic Number Ring

The study of prime numbers has been an area of interest in mathematics since antiquity. One natural question one may ask is "How many primes are there less than or equal to some positive integer?" The first attempts to answering this were in the late 1700s, culminating in the celebrated Prime Number Theorem. We investigate how this may be generalized to primes in an imaginary quadratic number rings in a given sector of the complex plane.