Quotients of Gaussian primes
Stephan Ramon Garcia
TL;DR
This paper investigates whether the set of all quotients of Gaussian primes is dense in the complex plane, extending the known density of prime quotients in the positive reals.
Contribution
It provides an answer to the open question of the density of Gaussian prime quotients in the complex plane.
Findings
The set of quotients of Gaussian primes is dense in the complex plane.
The result extends the understanding of prime quotient distributions beyond real numbers.
The paper confirms the density property for Gaussian primes, analogous to rational primes in reals.
Abstract
It has been observed many times, both in the Monthly and elsewhere, that the set of all quotients of prime numbers is dense in the positive real numbers. In this short note we answer the related question: "Is the set of all quotients of Gaussian primes dense in the complex plane?"
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Limits and Structures in Graph Theory