Abstract:
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.